How difficult is it to petition to relocate when the father has not exercised his visitation rights.

I have two kids in the state of ny. I am divorced. My ex husband is mentally ill and went to court last July to say he wished to not exercise his visitation rights. He hasn't spoken to or seen the girls in 10 months. My kids are very scared of him and are in counseling because of some emotional abuse that resulted from their visitation with him. I have been presented a great opportunity to relocate out of state for a job. My current husband (the girls step father) would love to adopt the girls but, knows their father won't willingly allow that. Will I be able to relocate? My kids are scared that he will ask for extended visitation to get back at me for leaving. Would a judge allow the move and allow extended visitation if he has not exercised any visitation or phone calls in almost a year. What do you think the outcome would be in family court? Thank you for your time.