co parenting, still married

My question is about co parenting. My husband decided he no longer wanted to stay together with me when I was 6 months pregnant with twins. We have an older son who is 6. He helped me out while I was on maternity leave and then he moved to a new place and we moved as well. He visits about twice a week but is saying since they are his kids he should get to see them too. He has his license revoked and just got his third dwi. He is not a bad father but I don't feel comfortable with them being alone with him especially in the place he is living I don't even know with who he is living. He says he wants to have the kids one or two days a week. He says I am being selfish by not bringing them over. We are still married so I am wondering does he have any eighths to the kids if he basically just walked out? It's not that I don't want him to see them but I just don't trust his judgement if I am not around. Am I being unreasonable for not wanting them over there? Does anyone know if infole for divorce would I most likely get full custody since he has a drinking problem. Any advice or ideas would be helpful. Thank you!