Sadly, I think poor Tommen is doomed, as karmic vengeance on House Lannister for the murder of Rhaenys (another royal child who loved kittens). Aegon will either order the boy's death himself, GRMM showing that Aegon has become as hard and cruel as his supposed Targaryen ancestors, or someone else will do it in Aegon's name or for Aegon's sake (Jon Connington, if still alive, would have no qualms, he has already vowed to wipe out all of Robert Baratheon's "blood", which could also include Shireen Baratheon). If Tommen manages to survive for a few more years, he will not be considered a child, and Daenerys will have him killed. Stannis and Melisandre probably have marked Tommen and Myrcella for death as well.
My money's on the Tyrells to kill Tommen and present his body to Aegon as the latter enters King's Landing, possibly as a bribe for a union with Margaery. Mace has always wanted his daughter to be queen.
The problem for any Iron Throne claimant, if he or she succeeds in seizing King's Landing and the Iron Throne and the rule of at least some of Westeros, in leaving Tommen alive, is that no matter how innocent and decent a child Tommen is, there will always be those who will rebel in his name. They might be able to leave Myrcella alone; though they should take her away from Dorne before any Dornishman-or Dornish boy - marries her, because according to Dornish law, she is the queen after Joffrey's death. If I were Aegon, I would at least contemplate marrying either Myrcella or Shireen once Tommen is dead. Another alternative would be allowing Myrcella to live as a celibate Septa or silent sister; she and her heirs could be dangerous if she is married to someone other than Aegon himself. And the flip side of Aegon marrying Myrcella; however charming and smart and good-hearted she is, she would still be regarded as either the Usurper's Daughter or incest-spawned bastard abomination; which would cast a shadow on any children she might give Aegon. If the Iron Throne's next holder decides that both Myrcella and Tommen can live as long as they will produce no children, Tommen can either become a Maester (I personally would not send a rival king to the Wall, where he might recruit an army, or someone else could recruit an army for him), or, cruelly, be castrated first to reduce the kid's likelihood of being used as a viable focus for rebellion; I doubt that anyone would risk their lives to put a eunuch on the Iron Throne.
Tommen is such a nice kid; who would, with better guidance than he's getting, grow up to be a good man. It's a shame, but I don't think he's going to get the chance to do so.
I don't think that Jaime is the most evil character in the series, but he is not a good man. He is an immoral person who has done one purely altruistic deed in his life - saving Brienne. (killing Aerys to stop the wildfire blowup was not an act of altruism, since Jaime was at risk for incineration as well). And I don't recall Jaime implying that he was at all worried about his children when he tried to murder Bran Stark; he thought primarily of Cersei and probably somewhat about his own neck.
I do enjoy reading Jaime's chapters; since he does have a certain amount of wit and irony in his narrative.
My coin's on the Tyrells; any of them, either actually murdering Tommen, ordering his murder, or not killing the boy but being blamed for the deed. I don't think GRRM named the family after the servant of Richard III who just happened to have confessed to murdering the Princes in the Tower by coincidence. (Tyrell/Sir James Tyrrell) GRRM is sufficiently knowledgeable about the Wars of the Roses, and probably their aftermath, that he was aware of Sir James being at least the nominal killer of the young boys)
Poor Tommen is going to be in the line of fire from many parties:
1. Aegon and/or his agents if he does take King's Landing, simply to cement Aegon's claim on the Iron Throne.
2. Daenerys and/or her agents if she takes King's Landing. I'm not sure that Dany would order the execution of a boy as young as Tommen for his family's crimes, but I doubt that Jorah and others among her lieutenants would be so scrupulous. Also, her dragons could just incinerate whatever part of the city or the palace that the kid happens to be in, not to mention Casterly Rock if Cersei and Tommen are holed up there.
3. The Sand Snakes get to him first. They're anxious to avenge their father's death and the deaths of their kindred Elia & Rhaenys and they're not too particular about which Lannister they slaughter, or how old the Lannister is.
4. As Aegon enters King's Landing, Mace Tyrell decides it's time to get a new son-in-law and liege and kills Tommen to present his body to the young conqueror as a dowry for Margaery.
5. Either Aegon or Dany, or both, are banging on the doors of Maegor's Holdfast, and Cersei blows the place up, with herself and Tommen inside, utilizing her hidden wildfire caches, rather than have herself and her son taken alive.
Mel will drop poor Stannis like a hot potato as soon as she figures out that AA is much more likely to be Jon than Stan. It looks like Rhlorr is really trying hard to tell Mel that AA is Jon, when she's praying for guidance to Rhlorr in the matter of AA and getting visions of snow (either actual snow or Jon Snow, can't remember, but it was in DANCE OF DRAGONS I think).
Wasn't Rhaegar convinced, according to Dany's vision in the House of the Undying, that baby Aegon was the PTWP? Which looks extremely unlikely, curretn-Aegon being a callow brat who may or may not claim the Iron Throne but probably has little chance of holding it, not to mention there being doubts that he is actually Rhaegar's son?
I'm not totally discounting all the prophecies; but so far they either have failed to come true (Rhaego not being born alive, much less becoming the Stallion Who Mounts the World) or come true in weird, hard to anticipate, ways (Sansa did not actually have snakes in her hair per the witch's dream, but she brought poison to a king's wedding; and we still don't know if Sansa will accomplish the death of a giant, i.e. Gregor, or a person whose family had a giant as a sigil - Littlefinger - or push Robin down because he was being a 'giant' destroying her snow castle...or possibly kill Robin on Littlefinger's orders).
I think Jon is the most likely candidate to be AA/TPTWP, but I still wonder if Theon could become AA (and sacrifice either Jeyne Poole or Asha if a repeat of Nissa Nissa is necessary).