(I hope that my ideas are solid 
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2) The second rebellion is a more dangerous one. When it broke out, in 207 BC, the country suffered from Ptolemy IV's mismanagement and an economic downturn caused by the 2nd Punic War, which shut down trade with southern Italy, Sicily and Carthage, which was perhaps the largest part of foreign trade in Ptolemaic Egypt. But more importantly, there were many locals with recent battle experience (Raphia in 217 BC.) and who knew how a hellenistic army fought. Thus, the rebellion itself was more threatening, while the government was weak and divided. If things really go down, then there is an actual chance that, by 205/204 BC, the rebels could control almost the entire country.
This means that Ptolemaic outer territories (especially Coele Syria) would be even more vulnerable than OTL. Thus, when Antiochus III invades the latter, he faces only token resistance and certainly not a response like Skopas' offensive during the winter of 201-200 BC. that prolonged the conflict. Also, Egypt is most certainly in chaos after the rebellion. This may prompt Antiochus to invade Egypt itself in 204 BC (although Egypt is not a part of the Seleucid patrimony, whose total reclamation was Antiochus' goal, Antiochus may think that it is too good an opportunity to miss). The locals would fight, sometimes to the bitter end perhaps, to fend off this offensive. But most likely, they will be defeated, and after one or two years of fighting, Egypt is controlled by the Seleucids.
Antiochus could choose to make Egypt a client state of his, under a scion of the Ptolemaic dynasty. This would spare him the potential trouble of pacification and would be more in line with his methods in the East, where he allowed the rulers of Parthia and Bactria to remain independent but under his suzerainty. But he could also be worried about a Ptolemaic resurgence that could threaten the Seleucids in the future, and Egypt is much closer to Antioch and much wealthier than Parthia or Bactria, thus direct control could be considered preferable to indirect rule.
Judging from the administrative organisation the Seleucids imposed in Coele Syria, Antiochus would most likely impose a far less controlling administration than what the Ptolemaic one had been. The locals would receive certain freedoms and a limited degree of autonomy, as a "nation" within the Seleucid realm. There will be a continuation of the previous economic system, where the king controls most of the land and thus a large part of the economy, but a large number of the regulations that were previously in place would be dropped. This would help with stability, as farmers wouldn't be as pressed by a non-adjusting tax burden and the rather exploitative system that was the rule before and consequently, they would be able to meet their obligations with greater ease. Therefore, we could expect that Seleucid rule would be fairly secure in these first years.
Rome may react, but apart from a diplomatic demonstration/presentation, it couldn't do much more. It would still be embroiled in the 2nd Punic War (as it is 204/203 BC and I think it would be rather difficult to end the war earlier than OTL in this last stage of it). When Rome manages to force Carthage to sign the peace treaty and turn its attention eastwards however (we could expect that Philip V of Macedonia would still embark on his quest to capture the whole Aegean region, in accordance to a deal like the famous "secret pact" he had formed IOTL with Antiochus, that Attalus I of Pergamum and Rhodes would scream bloody murder and ask Rome for help and that something small like the OTL affair of the Akarnanians that has betrayed the Eleusinian Mysteries would be enough to trigger a general conflict in Greece). However, this time Rome may be forced to be more diplomatic and thus actually try to negotiate instead of forcing Philip to go to war, as Antiochus isn't preoccupied in Coele Syria ITTL and therefore, he may intervene on behalf of his ally/"ally" and many in Rome would be unwilling to enter another potentially long war. For his part, I think that Philip V would accept a negotiated settlement; if he doesn't do anything like his OTL Abydus stunt, then war would have been temporarily averted (let's say for 2-3 years).
During that period, Philip would most likely continue his operations in the Aegean, although he would be more cautious and limit his attacks on Ptolemaic territories in the Aegean. He could make some more gains than OTL (some minor cities in Ionia, the island of Lesbos, perhaps the rest of the Cyclades - if the Rhodians retreat from the area). Meanwhile, his opponents would try to stop his advances, by installing garrisons to some of the last remnants of Ptolemaic presence in the area that are strategically important to them and trying to get the neutrals in the Aegean and the Aetolians to form an alliance against Philip.
At the same time, Antiochus has 2-3 years free of other entanglements, unlike OTL. I think that he would use this time to strengthen his reforms and consolidate his eastern gains, as well his conquests in Coele Syria and Egypt. Antiochus would also launch operations in Asia Minor and capture the Ptolemaic territories in Cilicia and Pamphylia (if they hadn't already surrendered following the collapse of central authority). In western Asia Minor, Antiochus would have a harder time, as Rhodes and Pergamum were equally opposed to Philip and him (Pergamum also had been, for a long time, somewhat adversarial to the Seleucids, since the Attalids vied for control of the Seleucid territories in Asia Minor and had intervened in their civil wars).
There could also be attempts to dislodge the remnants of the Ptolemaic dynasty from Cyrenaica, where it would most likely have retreated. Assuming that Ptolemy IV is dead and that he killed the same people as IOTL, then Antiochus may consider it a good idea to give Cyrenaica to a lesser, surviving member of the dynasty (perhaps the branch that IOTL controlled the area of Telmyssus in southwestern Asia Minor). However, in the long term, this could be a really bad idea, especially if Antiochus IV gets on the throne and has the same ideas like OTL, since an uncompromising Hellenisation campaign would cause rebellions in Egypt that the scions of the Ptolemaic dynasty would try to benefit from to reclaim their lost kingdom. Also, Antiochus would possibly consider such an arrangement unnecessary and annex this last remnant of the Ptolemaic realm, in which case the remaining members of the dynasty would have to seek sanctuary somewhere.
Thus, by 197 BC. things could lead to war. Rome has managed to largely recover from the previous war and its more warlike faction has regained influence. Most of its allies in Greece and Asia Minor ask for it to intervene against Philip, Antiochus or both. The Ptolemies could also send emissaries to ask for help against Antiochus, stressing his alliance with Philip.
The Senate would be in a difficult position, since it could potentially have to fight most of the Hellenistic East and the most powerful monarch of his time. Therefore I think that they would try to secure Antiochus' neutrality, by all means necessary, before they would start dealing with Philip (they could promise him Philip's holdings in Asia Minor in exchange). Rhodes and Pergamum, although not very happy about such an arrangement, they could tolerate it in order to deal with Philip. There are two potential outcomes :
1) Antiochus would of course love such a deal and he would most likely take it. The rest would most likely happen like OTL : the Romans and their allies declare war, Philip fights but ultimately loses. There may be a more moderate peace treaty, as the Romans wouldn't want to make Antiochus worried and, perhaps, because they wouldn't want to antagonise Philip so much that, in case of a war with Antiochus, Macedonia would side with the Seleucids (although the latter possibility could be also an argument in favor of a equally harsh or harsher treaty than OTL, I don't think it would be likely). Antiochus gets what he was promised. Given the fact that he has been even more successful than OTL, I think that he would press for the restoration of Seleucid control of the Hellesponte and Thrace, which were the Roman red line in the negotiations. Therefore, an analogue to the Antiochic War could very well happen ITTL too.
In this case, Antiochus is in a rather better starting position, since he has had an earlier headstart in creating his navy (likely 5 or 4 years earlier than OTL) and his operations in Asia Minor (at least 3 years). He also has greater prestige as a political and military leader, while the fact that he is considered even more powerful than OTL may prompt the Romans to maintain their troops in Greece longer, something that would make anti-Roman feelings more prevalent and increase pro-Antiochus ones. Combined with a milder peace that probably didn't decimate his military capabilities as extensively as OTL, this might lead Philip V to set aside the bitterness from Antiochus' opportunistic neutrality during his war against the Romans and agree to work with the former against the latter. This however would demand very delicate diplomacy on Antiochus' part, in order to be able to maintain his diverse coalition in Greece (it would be very difficult to have the Aetolians and Macedonia on the same side). Therefore, it would be more likely for Philip to side with a Rome that is very short of allies in Greece.
Once the war breaks out, it is very difficult to say whether Antiochus could win or not. The addition of Egypt to his domains would increase his power considerably, therefore increasing his chances of victory. On the other hand, if he were to do something like raising taxes, Egypt could rise up in revolt against his rule and tie down troops that could be deployed in Asia Minor and Greece, while the experience from Egypt's conquest could make Antiochus worried about the loyalty of native troops, which would force him to work with a smaller army (although a smaller, more integrated and easily controlled army has its benefits).
If Antiochus loses the war, then the situation may develop in a way similar to OTL, although with a much milder peace treaty (because the real treaty of Apamea was really an ASB moment, and Antiochus is in a relatively stronger position). With a (much) smaller indemnity to pay and fewer restrictions, Antiochus would be much less under pressure to find money, which will avert the attempted raid of the temple of Velus in Elymais and his early death and will leave the Seleucid state more robust and stable. Antiochus would probably turn his attention to the internal reorganisation and reforms and perhaps a new campaign in the East, perhaps in an effort to strengthen Seleucid control there. These, potentially combined with continued control of Egypt and Cyprus (since the Ptolemies weren't very closely related to Rome IOTL until ca. 168 BC. and ITTL they are without a powebase), the Antiochus could gradually prepare for a second round against Rome.
If Antiochus wins the war (possibly by taking a much larger army with him in Greece and crashing the Ronan forces quickly, then heeding to Hannibal's advice to consolidate his position in Greece while his fleet attacks the Romans near Italy and perhaps even carry the war on Italian soil-or threaten to do so) then Rome's influence in the eastern Mediterranean will be diminished for some time at least. The Romans will try to limit Antiochus' influence in Greece by supporting its few remaining allies (particularly Macedonia, which now is more threatened from the Seleucids, who could try to restore Alexander's empire). Rome would temporarily turn its attention to the west, while waiting for a moment of weakness for the Seleucids to strike eastwards. As far as the Seleucids are concerned, the victory would make them stronger; but with their interest more focused on the west of their realm, there is a possibility of the eastern satrapies slipping from their control again.
2) Antiochus refuses the deal, due to Rome's continued support for the Attalids. Philip then perhaps tries to get Antiochus on his side by offering him certain territories in western Asia Minor. Antiochus agrees and declares his support for Philip. Rome is unwilling to take on the two most powerful hellenistic kings at the same time and temporarily backs down. This can avert war for some time. But Antiochus will continue his operations in Asia Minor, and he could actually ask that Phillip give up any remaining possessions of his in the area. This could be the beginning of a diplomatic realignment, as Philip is now pressed by Antiochus and Pergamum and Rhodes consider Antiochus a potentially existential threat. Thus, these three could reach an understanding and form a united front against Antiochus. Antiochus may back down temporarily as well. If not, there may be a war between the two sides; in this case, if Rome enters the war against Antiochus, Philip will be unwilling to potentially disturb the balance of power and thus try to reach an agreement with Antiochus, who would likely accept the idea. In the end, there could be a negotiated peace, which would make some territorial arrangements in Ionia but would keep the status quo.