Is it permissible to abandon one's wife because of a female in-law who abuses her psychologically and physically, and does that affect the validity of the fast?

If a woman is ill-mannered and causes harm, there is no sin in boycotting her to دفع her harm, because boycotting someone whose religious or worldly harm is feared is permissible. Scholars have unanimously agreed on the permissibility of boycotting for more than three days for these reasons. If she shows a sincere desire for reconciliation, then she should be reconciled with and forgiven, out of consideration for the marital relationship which the Sharia has magnified. Boycotting her is lawful and does not affect your fast.