I want to know if I can move in to my Mothers house. My Dad has passed away and she is in a nursing home. Their savings pays the nursing home bill.

That is a possibility, but steps can be taken to prevent this from happening.  At some point, it is possible for the State to look at mom's residence as an available asset rather than as her "homestead" which is currently exempt.  Once the home is considered "available" and loses its homestead exemption, it will have to be sold and the money from the sale spent down in order for her to maintain eligibility.   As I said above, this certainly does not have to happen.  The house can be saved and steps can also be taken to save most of her remaining savings.  I would be happy to speak with you about your options.