The house can pass to you through probate. It does not have to be sold. You will, however, have to continue paying the mortgage after you acquire title to the property.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.
So long as the home is your (and presumably your mom's) homestead, it will pass to you if you are the named heir in her will or only heir if there is no will. Homestead property passes outside of probate. During probate, your attorney will request a Determination of Homestead, which will transfer the property into your name. So long as you continue to make payments on the mortgage (not sure what grant you are referring to), you will have no problems with the bank, although, they CAN accelerate the loan, it would not be in their interest to do so. Depending on the eventual size of her estate, you can file for a summary administration or, if her estate has grown appreciably, a formal administration.
My answer is of a general nature and should not be construed to be legal advice nor creating an attorney-client relationship. Carol Johnson Law Firm, P.A. practices in the area of Wills, Trusts, and Estates, Disability - with a particular focus on providing Special Needs Trusts for disabled children and adults.
Your mother should hire an experienced estate planning attorney to assist with her overall plan, including the home. If a proper plan is in place, it is possible to avoid substantial costs and delay in the title being transferred. The home should not need to be sold during the process. Be sure to continue to pay the mortgage, taxes, association maintenance and insurance during the transition after her death.
Answers to questions on this site are not intended to be specific legal advice nor create an attorney-client relationship. Hiring an attorney is a very important process which requires a high degree of diligence as well as entering into an agreement regarding the services to be provided and the fees to be charged.