Is it permissible for a Muslim woman to accept the gift of a house from her disbelieving mother if the mother will take out a usurious loan to purchase it?

It is permissible for you to accept the house that your disbelieving mother will give you as a gift, even if she purchased it with an interest-based loan, because accepting a gift from a disbeliever is permissible, and the interest-based loan pertains to her liability, not to the specific property itself.

However, if she is awaiting your approval to take a loan and buy the house, then it is not permissible for you to approve, as that would be assisting in something unlawful. You should advise her to stay away from usury and invite her to Islam.