Huh? Where do you get that?...never mind, I found it. His job is getting him a green card, therefore his wife should be able to get one too, and that solves the whole problem for the child.
Provided he doesn't put the green-card on hold until the divorce is over. If they divorce first, she has two options: get herself a visa on her own merits, or ...well, leave.
This is what concerns me:
The wife is already tossing "divorce" around. She apparently doesn't realize that divorce = go home (unless again she is able to obtain a visa herself). If she does realize this, there's just nothing compelling her to stay in the US with the child. This child has been raised in the US and while I realize that most kids can adapt fairly well to even a drastic change, when you add that to the fact that Dad will be staying here (in all likelihood), what lies in the best interest of the child?
What are the odds of the court actually allowing Mom and the US citizen child to return to Mom's home country with no guarantee of support, when the alternative is the child staying with Dad in the US where he can be supported financially?
Sure, IF Mom can stay with Dad long enough to get a greencard, the entire situation becomes tricky again. Even if she gets that residency, there's no guarantee whatsoever that she'd actually be able to remain the CP and earn enough to adequately provide for the child. OP didn't sponsor her, so she doesn't have that to fall back on. She's been out of the workforce for 7 years - more or less rules out everything but an entry-level job.
All else being equal, Mom has too much going against her. The "lesser of two evils" (in terms of the situation, not the parent) would appear to be - no matter what - the child being able to remain in the US. If Mom has no way of staying legally, I just cannot see the court ruling in her favor.