Can Mom use inheritance to pay down mortgage?

In CA, private caregiver help averages $25 per hour. Many questions have to be asked, depending on the situation and financial capacity to pay. Can your family afford to pay that for very long? When did your Mom move into a NH? When did your Mom receive her inheritance, before or after Medicaid eligibility?

I agree, to your assessment of SNFs to a point. I think it also depends upon the facilities in your area - how much competition they have, etc. And, one should always keep in mind, the caregivers are all paid about the same amount. The "country club" atmosphere at some places is just that, atmosphere.
Ask about caregiver to resident ratio wherever you go.
Our county home, while no-frills in terms of decor and cuisine, has a reputation for care that is comparable to the nicest facilities. I know a resident whose wealthy relative moved him from the county home to a very expensive SNF. He moved himself back. He felt more comfortable with the residents at the county home.
Nowadays, in the hierarchy of facilities, SNFs are truly "God's waiting room." More active people choose AL or Personal Care. However, county facilities tend to have residents whose income puts them out of the market for ALs (depending upon the state). When they need care, no matter how little, they have to go to a SNF that accepts Medicaid. In our state, that has resulted in the county home having a less frail (and consequently more 'fun') population of residents that the fanciest of SNFs.

You are better off to keep her on private pay for a longer time. We found out that the more reserve you have for private pay, the better your choices are for a NH facility. The high-end facilities are private pay only and quite expensive. Middle Class facilities will do private pay or Medicaid, but they look at your finances and would prefer you can private pay for two years, because the government takes so long to process applications. Finally you have the all Medicaid facilities, that are pretty dreary (an understatement) with minimal staffing and the food looks like a school lunch.

Spend an hour with an elder law attorney. There are lots of other issues involved in this question...did you take care of mom and, if so, for how long...is your name on the deed...which state do you live in...lots to take into account. Generally speaking, there's a 'lookback' of five years when a person goes on Medicaid.
If your mom has the assets needed to pay down a mortgage, I'm wondering how she qualified for Medicaid in the first place. Do you mean she's now on Medicare in the nursing home and will be applying for Medicaid once her funds are spent down?