This is how I think it works... keep in mind, I've never done this myself, but this is my understanding.
When you take on a rebel leader in your group you automatically go to war with the main faction (in your example, you'd go to war with the Vaegirs). You are considered the leader of this faction; you control any lords who might join you and how to distribute any fiefs you capture. Once the main faction is eliminated, you turn control of the faction over to the claimant and become a regular lord of the faction.
If you abandon the quest to overthrow the old king in the middle, your claimant will leave your party and YOU will be in charge of the rebel faction now, permanently.
I don't think there is a way in the game, without modding or cheating, to add extra factions that you don't control.