I don't think The Brotherhood is going to give them much of a choice.
Its personal by that point. In addition, I'm sure they'll find the need to protect the Synths against The Brotherhood re-invasion.
For The Railroad and Minutemen, certainly. Neither has a proper defensive stratagem against a Brotherhood resurgent.
The Institute? Piece of cake. Father specially crafts the attack on Logan Airport to send a message to the Brotherhood: come at us, and we'll turn your own best weapons against you. Its not enough to simply destroy The Prydwen, as he points out, but actually taking control of Prime sends a far clearer ultimatum to The Brotherhood.
However, should they ignore that and return, they have few avenues of attack. Without Prime, they have no way into The Institute. And now with the nuclear reactor started, The Institute can maintain full-bore Synth production indefinitely. Institute scientists also mention wanting to designhttp://i.imgur.com/kqEdwSp.jpg?1after seeing The Brotherhood's, and Advanced Systems already has an http://fallout.gamepedia.com/The_Institute_terminals#Plasma_Weaponry in the works. So now they've got hordes of power-armored Synths armed with Institute Plasma Rifles facing down the returning Brotherhood.