I know of another couple who, while not M, were in a R for about 4 years and had a young daughter (about 2yrs when they split). He was an alcoholic for most of his adult life (about 25 years) and finally became sober for about a year before his partner left him.
There could be a number of theories why your W (or this friend's partner) left once you became sober.
Of course, there is the possibility that your sobriety (which of course is a good thing) is causing you some stress and it is showing up in your M.
There's also the possibility that you USED to be FUN as a drunk. Now, you aren't fun any more. This can be the case when both partners are alcoholics or use alcohol as a reason to be fun with friends.
There's also the possibility that, while you were drinking your W was planning on leaving. Perhaps even had an A of some sort. Now that you are sober and more conscious of what is going on with the family, and her specifically, she can't "hide" what's going on so wants out.
And then there's the possibility that, now that you are sober, your W thinks that she does not have to protect you any more. Some spouses stay in a R for co-dependent reasons.
None of that really matters at this point, but you asked. Those are SOME reasons. Really, only your W knows why she's doing this. It may or may not have anything to do with your past as an alcoholic or your current sobriety.
That said, LRT is a possible technique for you to use right now. The question is, WHY do you think it's the technique for you, right now? Even though DR says to use it if the spouse has filed or has moved out or other drastic things have happened, one can still try other techniques, first.
As RT says above, GAL will be important, keep focused also on your kids and being the best dad you can be, and detach your emotions from her words or actions. If she's given you any complaints that are valid and had been persistent (other than your drinking), how could you 180 those complaints?