I’m doubting if the breakup is caused by mistrust alone other than the fact she don’t like the idea of gambling and seeing her spouse engaging in such activity makes it complicated, although the man is at fault here because sometimes sharing secrets with a close person might not get them upset rather hiding such from them makes it bad. In my opinion her choice of leaving sounds over reacting basically gambling is not bad compared to all kind of criminal act, at this point self discipline is needed when engaging in gambling activity well relationship built on lies might one day end on the wrong side.
Telling your spouse about something might also anger them, but it won't be to the point where the person will get angry when they discover it, as the anger won't only be for whateverthey just found out but also together with the betrayal they are going to feel as a result of not expecting such an act from their loved one, but it happens anyway…
I also think the woman overreacted for leaving unless there have been other things which contributed to that; if not, the best thing that could happen in such cases is where she will only get angry, and after a few days, they will talk over it and move on, which is what family is supposed to do.