How should one deal with the wife's mother (who is the questioner's paternal aunt) who constantly insults the questioner and his wife, knowing that attempts to reconcile with her have failed, that these problems stem from incitement by a relative of hers, and that this behavior affects the entire family and has led to the questioner, his wife, and their children discontinuing visits to her for 8 months?

You are not permitted to sever ties with your paternal aunt, nor is your wife permitted to abandon her mother. The one who truly maintains ties is he who reconnects with those who have cut him off. The occurrence of ill-treatment from relatives does not nullify their right to kinship ties. Strive to repel evil with good and separation with connection. If that does not prove beneficial, then seek assistance from someone who has influence over her to advise her.