When a Chassidus splits…

What’s the Halacha:
Can a child be thrown out of school because of a parent switching affiliations?
Is there an obligation to the child, or is a Yeshivah like any other private corporation that can do what it wants?
Can a wife be fired because of her husband’s actions?
If parents sign a document not to change affiliations, is it binding on the child?
How much damage is caused to a child when he/she is thrown out of school?
Historically, what effect does a Chassidus splitting have on family structure?