Is the sick aunt's reliance on the maid for personal hygiene, despite the presence of her married and nearby daughters, considered a form of disobedience from the daughters, and is it a condition that the maid be Muslim to clean the aunt?

This is considered a shortcoming in honoring one's mother, especially in her old age, which the Prophet, peace and blessings be upon him, urged. It is more fitting for her daughters to undertake her care themselves if they are able, even if they hire a maid for her, as the intention is to care for her and attend to her. It is not permissible to entrust a non-Muslim maid with her care, due to her untrustworthiness in seeing what is impermissible, and because a disbeliever is not allowed to look at what a Muslim woman is permitted to look at of another Muslim woman.