taking care of ailing mother is equal responsibility of all the siblings including your sister. it is wrong that she is not allowing your relatives to your home and not taking care of her mother in law. what about all your brother and sister including their spouses taking turns to take care of your mother who has raised all of you equal care.
why should she go to old home??
Did you stop any of her relatives for coming to your house in the past anytime? find out her grieviances. call the meeting of elders include all the your near family members to discuss.