Child Custody questions?

Ive been with the father) of my daughter for over 4 years.We were broken up when I found out I was pregnant because he was claiming he was following me.I tried to work it out.While he has been faithful about doctors visits and now faithful about visiting her in the NICU,he is not being responsible for her financially.My mom and I have spent hundreds of dollars on all the things she needs.Dad,maybe $100.We had decided to find a place together and had been looking for months but due to his bad rental history it has been exteremly hard.I finally found a place that I could get soley in my name,all he had to do was pay half the bills.My parents even agreed to pay part of the rent because it was more expensive that we had agreed upon.My parents even went out and bought us furniture.Then the day before we were going to move,he decides hes not ready.So Im tired of having the father of my child refuse to be finacially responsible.Ive decided I want to move 2 1/2 hours away to be with my parents.I can go to school and have a better life for me and my daughter.My ex signed the birth certificate.At the time I was thinking,well just in case I ever need to get child support.What I didnt think about was Im giving him power over the future of her.I know he will try to get custody,partly because he loves her but mostly out of controll.Hes already imposing on my time in the NICU,an excuse he uses as to why he can no longer work overtime to prepare for her homecoming.Hes even planning to take advantage of the overnight family room so that he can stay in the NICU all night.My biggest fear is that he will try to take her home from the NICU.Can he do that? My Mom says she can only be discharged to me,but he is the father.Reasons why he shouldnt get custody:Hes 43(almost 44),lives with his mom along with his other 3 brothers who my ex admit all actively do drugs.My ex is an ex cocaine user,clean for over a decade but still.Ive had to call the police myself on him in the past due to threats.He also has a record of communicating threats/intimidation.Also assualt on a female 20 years ago.He cant seem to find a place to live himself.Though I might also be living with my parents soon while Im out of work taking care of her upon discharge.Im also breastfeeding.Im NC,any advice?