Okay this is pretty complicated and I suspect there’s more to the story here. They should’ve went to a rabbi or beis din to work this out. There’s a difference between saying he doesn’t want the kids to be raised Chasidic and not being raised Jewish at all, i.e. other variants of Orthodox.
The mother shouldn’t be plastering lashon hara against the father on websites. That’s ridiculously harmful to the kids.
According to halacha, the parents are responsible to teach the children Torah and a trade to earn a living.
I agree. We're only hearing the mother's side. Perhaps his objection was more about the curriculum spending too much time on Talmudic studies, and not enough time preparing the kids for holding a job in the secular world and ensuring the kids can function outside the Chasidic community.
You may want to read the blog mentioned in the last line before writing some comments which are cruel and callous in this case. It’s one thing not to help kids who had their payos lobbed off by their father, one kid smeared with urine in his face (according to the oldest of the 4) and yes they were ripped from all religious observance and forced out of any religious school. It’s bad enough that people don’t want to help. When they cast doubt without even reading (the blog link is there for a reason) to prevent others from doing so, there are truly no words (other than fil rishus veinik mitzvos).