The parents are still legally married but no longer live together.can the father leave the state with the kids? there is a possibility of abuse from the mothers boyfriend.

Are they legally separated or informally separated? If they are informally separated then he can leave the state with them but she has as much right to go and bring them back. Do they live with him now? He would be better off going to court to first file for legal separation and custody than just leaving because that can cause things to get worse long before they get better.