Does a wife's mother deserve her father's anger if she welcomes her sister who fled from her brother, knowing that her father has forbidden this communication and is angry with anyone who welcomes her?

Boycotting ( hajr ) is a treatment that should only be resorted to if its benefit for the person being boycotted is highly probable. If boycotting the daughter has a positive effect on her and rectifies her, then the father's obedience in this regard is obligatory, because it is prescribed for those who commit sins, in order to deter them, just as the Prophet, peace and blessings be upon him, did with the three who stayed behind from the Battle of Tabuk. However, if boycotting leads to her corruption and increases her rebellion, then the father should be approached to change his approach, and perhaps leniency would be more beneficial than boycotting. If he insists, then he should not be informed of what the daughter does with her sister.