Child Custody and Unmarried?

I have a 10 month old daughter and her father went to jail about 3 months ago. Left me with nothing. I cant get a job because i need daycare but i need a job for daycare. So its a vicious cycle. Her father has a pretty bad record to begin with. 6 counts of burglary of a motor vehicle. He actually got arrested for hitting me when he was drunk while i was 2 months pregnant. And now he is in jail for threatening a cop. But i have no job, living at my mothers, cant drive because i have no liscense and it just seems like everything is going wrong. And i dont want to be w/ the father anymore. Because he had already stolen 1200 dollars from me and i was still dumb enough to stay with him. Then i found out he sold my computer monitor and lied to me about it the whole time and tried to sale my computer. and he's just a piece of **** i dont want anything to do w/ him besides him paying child support once he gets out and visit juniper. but the problem is my mother is an alcoholic but i dont let her hold her but i'm afraid he'll use that against me to get custody. i dont drink or smoke. i get up 8am every morning w/ my daughter. do i have any luck?