Carrying car insurance when mom no longer drives.

Mom with dementia has decided to stop driving. YAY! We have a caregiver come 1x/week and would like them to drive Mom's car to take Mom and Dad shopping, out to eat, etc. Their insurance carrier has said this is no problem as long as Mom retains her license(Dad gave his up years ago.). We would like to explore selling their car and having the caregiver use one of our cars. Our insurance is giving us a hard time on this which seems weird. The caregiver agency makes sure their caregivers retain valid insurance and are insured on any car driven, so that shouldn't be an issue. Has anyone else had caregivers drive one of their cars? If so, did you run into any issues with car insurance? Thanks!