Wa'alaikumsalam.
When my parents in-law were still alive I often enough bought something or gave money to them, including to pay hospital costs when they got sick. I did it because it was my duty as their son in-law.
If a man get married, then he has to treat and respect and love their parents in-law like his own parents. If he could not treat his parents in-law like this, then he is not a good husband.
Sister, the wife does not always must obey the husband. Tell your husband you will move only if your mother move with you too because you have to take care her. If your husband refuse it and give you choice to choose him or choose your mother, my advice is, choose your mother.