What is the ruling on staying, eating, and drinking at the home of a sister whose husband purchased her house with money mixed between lawful and unlawful sources, and is it permissible to pay money in exchange for food, and what is the ruling on taking money from her for medical treatment?

The money obtained from these restaurants is mixed, containing both lawful and unlawful elements. Dealing with its possessor by accepting a gift, present, or hospitality is only disliked (makrooh), not forbidden (haram (definition)). What you take from your sister for treatment is not forbidden for you, especially in times of necessity. It is better for you to try to find independent accommodation for your vacation, as it is further removed from benefiting from unlawful money and offers more privacy for both of you.