Step-parnet in need of help.

I have a 5 year old step child (G). Me and his father has had G ever since his 3rd birthday. G's mother pays no child support. She came down in April of 2011 and that was the 1st time she had seen him since May (2010) and that was the 1st time in a year. I want to adopte G. I love him like his is my child. Everyday since his 3rd birthday it has been me and him. I took him to his 1st day of Pre-K and KK. I take him to the doctor and make sure he gets what he needs. I am the one he comes to when ppl ask him to talk to his momma. When he lost his 2nd tooth he asked to call me his momma. But I know the real mother (J) will not sign the papers I will have to fight her. Do you think that I have a chance it getting my little boy to be 100% mine? J still lives with her mother, and never helps with anything.. but I dont need her help either. I just dont know what to do.