My abusive ex left me and my new baby when she was 2weeks old.. he hasn't bothererd with her for the whole of her 2 years... does he have any rights.. I want to get a court order for full parental control just in case he decides to show up in the future.. any advise please...

Yes, he still has rights until a court takes them away. In order to do this though, you need to be married and your husband willing to adopt your daughter.

Is there a child support order in place already ?