My xabf was sober for two years, then he relapsed, then he relapsed again, then he assured me he was committed to his recovery, and he relapsed again, said mean things, hurt my feelings a lot, I left him.
If she's so dramatic that she's threatening suicide, she's probably pretty manipulative and needs A LOT of counseling, and - not to be a negative Nelly - will probably relapse very soon.
Keep us posted though. It would be great to hear if things are working out and she goes to counseling and stays focused on her recovery.
Good luck. If I were you, I'd keep your kid out of it for at least a year, regardless of the alcoholism.