Your mum doesn't need to be the owner or registered keeper of the car to get insurance.

That said, not all companies will cover a driver who doesn't own the car, but there are lots who will. She must tell the policy provider who the legal owner and keeper is, however.

I fear things will be more complicated with your dad's insurance. His policy document will most likely insist that he informs his insurer of any changes in health or circumstance. Failure to do this may result in the policy being cancelled in the event of a claim.

In the first instance, I would advise that your father or mother speak to the vehicle's insurer to explain the situation as the existing policy may no longer be valid.