The ownership remains with the Ltd company but she was allowed to keep using it.
It sounds like a situation where the car is being provided by virtue of the driver's relationship to the director ... so the benefit is assessable on the director. Class 1A NICs will be payable in the usual way and running costs/capital allowances will remain available. There may even be an argument that the car was originally provided by virtue of Dad being a director - you have to consider whether a similar employee NOT related to a director would have had the benefit of a company car in their own right.
The alternative for a car provided by virtue of a family connection etc is that all costs and CAs are disallowed.
HMRC guidance starts here. http://www.hmrc.gov.uk/manuals/eimanual/EIM23550.htm
But some has been withheld.