Re: Where does one stay if your husband is out of town?
I think you should consider that your MIL doesn’t want you to feel uncomfortable in the house. Perhaps she even feels a bit guilty for leaving you given the circumstances, and so is asserting it’s your home in order to make sure you don’t feel like you have to leave.
As another poster said, stay at your parents if that’s what you prefer, but come by regularly for company/help/etc as needed.