Need some advice PLEASE!?

My brother was currently in prison for 3yrs he got out in sept of last year & now lives with my mom well for that whole time my mom had and still is taking care of my nephew which now is 6yrs old his mom lives less than 5 min away but still leaves him with her for whatever her reasons may be she’ll go pick him up every once in a while but you could basically say my mom is or at least considered his guardian but what irks me so much about the situation is while my mom is taking care of my nephew supporting him and all his mom runs to claim him when tax season comes around so she can have money to go on her little shopping sprees which I find very unfair I keep telling my mom to get custody of him but she says she isn’t sure if the courts would give it to her since there is no written statements or proof he’s been living with her this whole time and she doesn’t want to chance his mom getting scared and taking him away from us on the other hand my brother said he’d sign for her to have custody of him, what can she do? Is it even possible??