Rhaenyra's legitimacy is solid. It's her own succession that's subject to a shit-fight. The fact that Rhaneyra's children are bastards is an open secret. Even the show alluded to as much. As such, nobody is going to go along with a bastard ascending the throne. Especially with Viserys' trueborn sons still being around.

In that moment, Aegon, Aemond and Daeron's very existence becomes a threat, not to Rhaneyra, but her own heirs. So it's safe to assume once she ascend the throne, her children's competition would conveniently meet with a case of dead. This threat doubles itself after Daemon makes a comeback.

War was unavoidable the moment Rhaneyra gave birth to Jacaerys. It's a shame too because Jace is an upstanding lad. He singlehandedly leads the Black faction during the initial stages of the war and even managed to bag the North and he was only 14 years old.