How can one deal with the husband's mother who refuses to help her son with medical expenses from the inheritance, and how should the husband act towards her, and what is the legitimate ruling regarding the money remaining from selling the inheritance apartment and replacing it with a less expensive one?

The mother's right is great, and honoring her is among the most obligatory duties and the greatest acts of closeness to Allah. Part of honoring her is spending on her if she is in need of financial support. If the mother is well-off, then she ought to give her son his share of his father's inheritance. However, assisting him financially from her own money is not obligatory. There is no blame upon the son for asking her for his share of the inheritance, but it is not permissible for him to mistreat her or fall short in honoring her. If the mother sold the apartment she lives in after the father's death, then the difference in price between the two apartments is part of the inheritance, which all heirs are entitled to, unless they willingly relinquish it to her.