I don't imagine you're going to like my suggestion, but I'm going to suggest it anyway -- Time is your friend. The more time you are out of rehab, sober, and succeeding, the lower the risk of admitting you as a student will be.
If I were on an AdCom, I would have some concerns about an applicant who has been in rehab. Quite honestly, I would have far deeper concerns (sorry) about an applicant who has been in rehab twice. And I would absolutely want to hear the applicant's explanation for why stint #1 wasn't successful and why stint #2 will be. I'd want to see a good long 'safe' track record post-rehab to reassure me that you're up to the challenge of medical school. The more time that passes successfully after stint #2, the lower your risk as an applicant will be. (And the greater chance you will have at succeeding and not back-sliding.)
Kudos for what you have accomplished so far; and good luck to you OP. But I would also make plans for a 2-3 year Interim Plan B in case there are others who share my concerns.