Sometimes people get better. It's usually when they throw themselves into recovery and a lifelong plan with everything they have.
If she's gone to rehab and just found a person to replace the alcohol, then it doesn't sound like she's throwing herself into recovery.
But just so you're aware, recovery isn't a magic balm to fix a relationship. If you have never known her sober, she may not be someone you want to be in a relationship with. You may not be someone she wants to be in a relationship with. Recovery is selfish and may not leave her any emotional space for a relationship. There are about a million unknowns in circumstance of recovery that neither one of you can predict--and on top of that, unless she is willing and ready to work that recovery for the rest of her life, she will always be one drink away from relapse and picking up right where she left off.
But since it sounds like you're not dealing with a true recovery situation anyway, that isn't relevant yet.
The best thing you can do right now is focus on yourself, what losing or keeping this relationship would mean for you, and figuring out how to be the best dad you can be to those kids, who have a lot less choice about who is a part of their lives than you do. Growing up with an alcoholic role model (or a codependent one, for that matter) is pretty much the worst thing kids can endure in childhood and it will follow them in all of their interpersonal relationships until they eventually are forced to deal with it. Ask me how I know.