Is a man's moving out of his family's home to live separately with his wife and children considered an act of disobedience towards his mother who did not accept this, and what is the solution to this problem?

The pleasure of Allah is linked to the pleasure of one's parents, and disobeying them is among the gravest sins. You must try to please your mother as much as possible. If the situation cannot be rectified except by you and your wife moving out from your parents, then do so. This is not an act of disobedience to them, because the wife is not obliged to live with them. You must be keen on maintaining ties with them, sitting with them, honoring them, and treating them kindly.