I almost don't even think of this as an "affair"--as far as you were concerned the marriage was OVER, you weren't taking her back, you were separated, and the formalities had to wait until she was out of rehab. I don't think under those circumstances the vows are still binding--that's more a moral issue than anything else, and if you believe divorce isn't unforgivable you did nothing that appalls me, personally.
And yes, she went back to drinking because, in her mind, you would be waiting there like a faithful puppy when she came home, regardless of what she and her drinking have put you through. That was HER mistake. The return to drinking is on her, not you. If you made a mistake it was probably sharing with her that you had been with someone else.
Don't carry around the guilt of responsibility for her drinking. If you need counseling to become convinced of that and let it go, get it.