How do I file for divorce without opening up custody and visitation?

My husband and I have been apart and living in separate states for the past 11 years. We were married in the state of NY and I left my husband with whom I have an 11 and 18 years old with and moved to the state of VA 8 years ago. I have been looking to divorce my husband, but am afraid that if I petition for one it will open up custody and visitation all over again. He is a deadbeat dad and is truly unfit and has refused to sign any papers. My husband tried to stop my move to VA with the kids in which I won the case because the judge told him that he had made no effort with his kids when I lived 15 minutes away from him living in NY. He has made no effort to be in his girl’s life and suddenly is looking to after 11 years get visitation with his 11 years old that he does not know. Please advise how I go about getting a divorce since I am now living in VA and he is living in NY. Also please let me know if NY has any jurisdiction over making me bring my youngest to NY for visitation since he refuses to come to VA and only sees them if I bring them to NY.