Is it permissible to refrain from visiting the husband's family on the grounds of cost and the possibility of causing problems, especially given the mother-in-law's criticism of her physical condition? And is this considered a severance of the ties of kinship?

Among the virtues of a wife’s character are her kindness to her husband’s family, her overlooking their mistakes, and her assisting him in honoring his parents and maintaining ties of kinship. This will increase the husband's love and respect for his wife, and it will weigh heavily in the servant's scales on the Day of Resurrection. Allah the Almighty has encouraged us to respond to evil with good: "And not equal are the good deed and the bad. Repel [evil] with that which is better, and thereupon the one whom between you and him is enmity [will become] as though he was a devoted friend. But none is granted it except those who are patient, and none is granted it except one having a great portion [of good]."

Furthermore, forgiveness increases a servant's honor and is a path to attaining Allah’s forgiveness and pardon: "And let them pardon and overlook. Would you not like that Allah should forgive you? And Allah is Forgiving and Merciful."

However, if you are harmed or bothered by visiting your husband's family, there is no sin upon you for refraining from visiting them or reducing your visits, because there is no harm and no reciprocation of harm. Nevertheless, you are not permitted to prevent your children from visiting their father's family, as this constitutes cutting off ties of kinship. As for you, it is not considered cutting off ties of kinship if there is no relation between you and them.