Smackie is right, this guy is showing warning sign after warning sign after warning sign of being abusive and emotionally unstable. This is very different from just being jealous. GTFO now. Do your kids live with you? If so then that should be more motivation to leave if you actually give a fukk about your kids. If you don't then yeah stay with him and expose them to the shitstorm that you're in for if you stick around, let their experience with this so-called father figure fukk them up for life, hopefully you don't regret it until the day you die.
They see indoctrination and they call it "morality", "professionalism", or "maturity" depending on the context.