“Breaking up wont help the kids religiously. They will still see his religious behaviour, as he will still be their father.”
I agree, breaking up will make him drop any religious observence he still keeps and the kids will be exposed to that even if he is out of the house.
“(I always have to remind him on shabbos, and he always has some excuse why it’s not a good time/the kids need us, etc.).”
Whather its right or wrong, trying to be your husbands mashgiach never works, if anything it will push him farther away, do your thing – bentch with kavana and hopefully it will rub off on him (or at least at the children). Dont try to take care of the ishues he has with G-d/religion, however when it comes to the way he treats YOU then you must take a stand.