Your children will be fine. My mother kicked my alcoholic father out when I was 12.. bad time to lose a dad, and I did love him, but it was the best thing that ever happened. I had the best high school life ever, not being afraid of having friends over, or the unpredictability of "is he drinking or not??" I thank my mother every day (in my prayers as she's no longer aliver) for that courageous decision.
One of the most useful pieces of advice I ever got was "detach yourself from the results." In other words, do what you have to do, move forward, and don't think about the "what if's." If you do the right thing, all will work out.