What is the ruling on using magic to prevent a mother from frequently going out in a way that raises suspicions, given her rejection of advice and the children's fear of using force, and is this considered necessary to avoid the family's destruction?

Children must advise their mother gently if they see her leaving the house without a valid reason. If she does not respond, they are permitted to restrain her, provided this does not lead to a greater harm. Enforcing change by hand is for one's wife, child, and the like.

As for resorting to magic, it is forbidden and a major sin.