Is a responsible woman sinful for refusing to let her mother live with her, despite having cared for her for more than half a month after her father's death?

Taking care of a needy mother and serving her is obligatory upon all children according to their ability. If the daughter fulfills her duty towards her mother, and the mother does not need to live with her, then the daughter's refusal to have her mother live with her is not a sin. However, if there is no harm to the daughter in housing her mother, then it is preferable that she house her, especially if the mother has no other daughter to live with. For the mother is a gate to Paradise, and she is the most deserving of good companionship.