US citizen wants to divorce temp. resident. What about my kids?

I am a U.S. citizen and I got married a little over 2 years ago to a Japanese citizen whom I was dating for 2 years prior. Since we got married we have 2 beautiful babies.
My wife now has a temporary green card.
Things are not well right now, I believe my wife is pushing for us to relocate to Japan, which I am not ready to do as my Mom is pretty sick and I want to be here for her.
Also, my wife is becoming verbally abusive towards our children. Not physically, not yet. I fear for them when I go to work; I work pretty long hours as sole provider.
What should I do?
If my wife doesn't feel the love anymore I am more than happy for us to go our separate ways. But of course I am mostly concerned about my babies.
I don't know legal protocol on this. My kids are U.S. citizens but they have Japanese passports as well. If I get divorced I am sure my wife wants to go back to Japan. Will she get custody because she is the mother? Can they award two U.S. citizens to a resident to take abroad?
Where can I turn to for help with this??????