I have had custody (an agreement between my ex and I...no courts) of our?

Child since she left me a few years ago...since then we have both moved on and we both have toddlers with our new partners...she has always been in his life but ever since my gf moved in a year and a half ago she has de died she wants to go to court to actual custody...joint custody...she wants every weekend...she lives out of the city now....she as never paid child support to me since it was never ordered but has paid his way when she had him in her care...she is a stay home mom and I want to go after her for child support...but she makes no money and lives with her bf of 4 years,can I go after him for it and do u think she will get her half custody if she tries for it...