Make sure you have high relations with them. You should've raised your relations with opposing factions before splitting off.

Maybe someone else will provide more tips. :D

Go to rebel leader and you can pay them for peace alot of $$

At the moment you make your own faction you better be ready to face whatever foes you might face, because making peace is impossible. The way module works is that you can only make peace when you are neutral, not siding with a faction and dont have any land. After you control a piece of land, a battlestation, outpost, city planet you are considered as a lord. You know what they say when you ask for peace "you are a lord with no loyalty to anyone but yourself, no ruler will accept a lasting peace with you."
Basicly you are not considered a true ruler but more like a robber baron.