Right now she is paying her own nursing home expenses, but eventually her money will run out. When that happens we will sell her house to keep paying her expenses. Will Medicaid look back and penalize her because of the expenses of keeping the house while she did not live there? (taxes, insurance, utilities)
Remember that insurers do not look kindly on being asked to insure a vacant house, and if they do, it will cost more for coverage. And an empty house does deteriorate a bit even if it's not lived in constantly.
So you or your mother would be paying out expenses on the house while she's in the NH, until the house needs to be sold. What's the real estate market like for her home now? If it's good and the house is sold now, that's income now to be invested and no maintenance or obligations for someone to take care of the house - lawn, snow removal, cleaning, repair, etc.
While mom is private pay, she can spend her $$ to get a face lift or get new appliances - now whether that the best way to spend $$ is another issue.
If plan agreed upon is to sell, if it's not listed right now, why a wait?