First, why have you not divorced the not-so-ex, ex? Five years, a new boyfriend and child, and still no divorce?
The ex is lucky as he could find himself legally responsible for your boyfriend's child with you because he is the presumed parent until paternity is otherwise legally established with the boyfriend. I would have thought he would have run to divorce court when you ended up pregnant just to avoid additional liability.
Second, you went from a guy with a past to a guy on parole?? He is a "good person" but has been put in prison for stealing cars? Miss, let me tell you that no one goes to prison for stealing one or two cars ... if he went to prison it was because he had much more serious crimes that were plead DOWN to felony auto theft with prison time, or he has a far more extensive criminal history. It wouldn't have been carjacking, would it? In any event, this may not be the wisest choice of a new partner. But, I am sure you have heard that and choose to see the "good person" in him that is trying to get out.
Oh, and he did not go back to prison for spitting on the ex's girlfriend's car. Try again.
You and your daughter need to enter into counseling if she is acting out. Maybe all of you need to go into some form of counseling. It may also be time to close the door on the marriage and be done with it. Maybe that kind of finality will lend itself to a new beginning for all of you.
I can understand your ex not wanting his daughter exposed to a parolee. I wouldn't like it either. And it may well be that he can take you to court and seek custody of her as a result of this relationship with the new boyfriend. Your ex's past is neither here nor there because, apparently, the court did not even consider the matter so it is a legal non-starter. However, a court will see your boyfriend's criminal past and if it is extensive or violent (which is likely) they may well agree with a petition from the ex to gain custody of your daughter.
You might also consider some counseling for yourself to try and sort out what is best for you, and for your children. Never ending drama and a step-dad and daddy that is in and out of prison is no a good thing for you or the children. Time to sit back, get sme perspective, and figure out where you want to go.
Good luck.