What is the ruling on taking money sent from a sister who works as a domestic helper in Italy and misses prayers due to her work, and is she obligated to search for another job despite her difficult situation?

If your sister's work is permissible, there is no objection to benefiting from the money she sends to her family, because it is in exchange for her work and not in exchange for her abandoning prayer. This is known as "disconnection of the aspects." However, you must advise her that delaying prayer beyond its time is a grave sin, based on the Almighty's saying: "So woe to those who pray [But] who are heedless of their prayer." Work is not an excuse for delaying prayer, and she must repent and return to her family, due to the dangers of her remaining in her country.