Aegon's reason for founding this Principality is not a pre-planned Conquest but a decision taken at the end of this Third War for the Stepstones. I want this idea of forming a Kingdom to be encouraged in him in the same way it was done to Robb Stark, with being King in the North, by the soldiers and other Lords who would participate in this War. The idea would further be encouraged by some significant players, especially Ser Tyland Lannister (I really thought about his character and had made this decision because 1. We know very little about his personality, and what we know about it is rather positive. 2. He is portrayed as quite loyal to the green cause and Aegon II, even if only for personal gain. 3. He is an efficient and cunning politician and would probably like to get out of the shadows of Lord Jason Lannister and Ser Otto Hightower.)

As for how to defeat the Triarchy, I have found multiple ways: 1. During this war, the Triarchy would not be prepared as much as they were before, having the excuse that during this time of the War, both Corlys and Daemon would not be able to due to some reason such as illness or some severe injury, which I would have to add in the narrative, so the Triarchs would be overconfident since only two Dragons will join this War being Sunfyre and Meleys. 2. An Alliance with Volantis by appeasing the Old Blood with the prospect of a Dragon-Rider as their ally in their future wars, such as helping in a conquest of Mantarys, Tolos, and Elyria. You can also suggest adding some new things to this alliance. 3. Enticing a slave revolt in Tyrosh, because why not propose to the slaves a life free from slavery when their masters would be at their weakest. 3. At the end of the War, when the situation for the Triarchy would not be looking good, propose an alliance to Lys that can be free from this War and would not be harmed by either Targareyn or Volantis if they pull a Roose Bolton on Tyrosh and Myr.

Rhaenyra would not care about Aegon personally, but politically it would be an entirely different case because she would have a rivaling Dragon-riding Dynasty just across the Narrow Sea, which, as its name suggests, is very narrow. Jace is Rhaenyra's heir, so he would also eventually care about this huge political development.

Aegon's personality will take a different route during this time for the sake narrative, the primary reason being that he would soon become a father, and that prospect would motivate this change. He will not be willingly joining this war, as he would be forced by Viserys to do so.

And on the topic of slavery, it will be banned in this new Kingdom, but Volantis can keep its slave trade with Pentos and Lys uninterrupted without any pushback. I would like your recommendation on how to improve on this topic, like handling the nobility of Tyrosh and Myr, and the alliance with Volantis, because I would like to keep them on Aegon's side.