Just don't discuss her at all. You should be happy that your ex-wife has found a new mate. Her life with you must have been difficult to say the least, and for her, the new man is her happy ending. Perhaps some day, in your new condition of sobriety your paths may cross and you can be civil to one another. I hope so.
Time does heal old wounds.
But your main object now is to rediscover your children. You don't need to plead with them, or to give them any lurid details of your past misdeeds, or the problems you have had to recover. Just tell them you are now finished with the problems you used to suffer and that you feel it would enrich everyone's lives, theirs and yours, to be able to get back on friendly terms. Keep it light. If your own home is not suitable to entertain them, suggest a meeting at a restaurant.