Is it permissible for a woman to hire a housemaid for her deceased husband's mother from her own money, knowing that the mother is unaware of this and will refuse, and that she is in dire need of the housemaid?

The woman's case must be referred to the ruler or his deputy, such as the Sharia (definition) judge, and her funds may not be managed except by his order, based on the hadith (definition): "The ruler is the guardian of whoever has no guardian." So, if the judge entrusts her affairs to your mother, she is permitted to manage her funds as she deems beneficial. If he entrusts it to someone else, the money must be handed over to the person specified by the judge. We call upon her children to fear Allah and take care of her.