My sister takes care of our mother and her doctor has advised to put her in a home.

The hospital that your mother is in should have a social worker on staff and discharge planners - people that have to be sure that your mother is not sent away to an unsafe environment.

https://www.yes.state.nm.us/yesnm/home/index is the website portal to find out what benefits your parent qualifies for. MediCARE doesn't pay for custodial care in a nursing home; MediCAID would be the program that she would have to qualify for. It's possible that some information on the MediCAID application was incorrect - if she only gets $1000 per month it should be withing MediCAID guidelines. I suggest talking with a social worker to see if they've got a list of nursing homes that (1) accept MediCAID pending since your mother is not approved yet and (2) have someone familiar with the social system in New Mexico that can help your sister apply for MediCAID in New Mexico. MediCARE would not be involved in putting your parent in a nursing home because they pay for hospitals and doctors, not the daily custodial care of a nursing home. Be aware that if your mother gave away money or assets over the last 3-5 years, that may be part of the problem for her being qualified for MediCAID. The eligibility for benefits and applications to get started are all online.