Mom with dementia in private group care home is insisting she needs to go to the dentist. Says her teeth feel funny. She is barely mobile.

Yes. Tooth infections can spread to the brain. Oral hygiene is so important that even my 94 year old dad's urologist inquires about his oral care at check ups. Medications can affect teeth and gums and she is ver likely not taking good care of her teeth on a daily basis. My MIL was discovered to have an abscess when she was in the hospital for an unrelated reason and they had it pulled.
If you were closer to Tucson I would provide you with the name of a super dentist who is great with elderly patients.... check into mobile dental clinics, too.