Me and my boyfriend is getting married on may 28 and he wants to adopt both my kids. Can he even if I have a order of protection against the father and full custody of the kids

The specifics depend on the adoption laws of whichever state or country you are in.

But, in general, yes. Once you are married (In some places, you have to have been married for a certain period.), he can apply to adopt your children. Their father normally will need to be given notice an an opportunity to object. Consult an attorney in your jurisdiction about the details.