I've been in your situation in the past, OP, albeit with an ex boyfriend so no family ties.
As with your H, my ex was drunk and "this girl" (she certainly does get about, doesn't she?) just lunged at him, completely unsolicited, and he "didn't pull back quickly enough."
Because I was 21, desperate to be the "cool girl" and really liked him, I too tried to get past it despite thinking his story was utter BS. Unfortunately, as you say, I could never fully trust him again, I was always on edge and I didn't like the person I was becoming.
The relationship finished when I ended up cheating on him - more out of insecurity and revenge than any real feeling for the other guy (21 and stupid, remember?).
Even now, married with 2 kids, mortgage etc., this would be a dealbreaker for me. I'm sorry. 