I am an older nanny, probably the age of your mother, OP, and I would have no problem washing your underwear (in the machine, of course).
If a person has reasonable personal hygiene habits, I don;t see the big deal.
And, OP, I am sorry you are going through a tough time. Yes, as a nanny, I would do more for a single mother who was in a tough transitional time in her life.