okay...Meth...possesion/use or manufacture or delivery. It does make a difference as possesion/use and even delivery is bad, but not as bad as manufacturing. Mostly because Meth labs have a nasty habit of blowing up.
Find out, it may matter and DEFINITELY talk to a lawyer, but keep in mind you will have to prove also that the father can provide a better environment. Find out why he doesn't have custody to begin with. Also keep in mind he's probably still on parole and there will be a parole agent involved. Look into that as that could be a strong factor. If the parole agent says the guy is in compliance with his parole and doing everything he is supposed to do, it may take some of the wind out of your sails.
I'm not saying what I think is right, just what is most likely to happen. In my opinion, mother SHOULD lose custody for simply exposing her child to a felon. It is bad enough when one of the bio parents is a felon, there is no choice for the kid. But when it is an 'siginificant other', not even a step parent, mother should be shot for choosing someone with an obvioulsy stellar track record over what is in the best interest of her kids. Like I said though, if this guy has truly turned his life around and his parole agent is willing to state that, it may be a hard sell to a judge. You know, having paid his debt to society and all.