Oh my God my man I wish you the best and to have the wisest decision. I would talk to a therapist regarding what would be the best course or action if she does return in six months. I personally would most likely 80% certain not take her back. She made her bed she needs to lay in it. But than again there are the children to take care of. But honestly I think it would be more logical to minimize the negative influence that their mom might have on them. They don't need to see both the substance infidelity and then the physical infidelity. That's not an example you want them to have.
Personally I am kind of glad I didn't go to rehab since I've read all of those rehab romances which are sickening since they strike at the most vulnerable mental states. I am already too chemically ****** up with my alcoholism to let another thing take place of booze. That's just filling one dopamine rush with another. Filling the loss of booze with the gain of "love" where in reality both are transitory.