90 days on pre-reg cars

The dealer shouldn’t be handing the car over to a customer before the 90-day period is up.
Pre-registered cars have to be kept by the dealer for 90 days before they can be sold. If the dealer wants to sell the car before then, they can’t claim any money from the manufacturer and they’d have to charge full price for it, rather than the discounted price you’d expect to pay for a pre-reg car.
In terms of resolving your daughter’s immediate issue, the dealer should be insuring the car while they still have the V5C registration book.
Ownership of the car is potentially a messy issue. Check the dates that the dealer has put on the contract – they may have forward-dated the paperwork to the 90-day point.
And yes, this should have all been explained to her before she bought the car.
I don’t know the legal issues involved (I’d suggest visiting the forum at legalbeagles.info for some legal advice), but it’s not good practice to deceive your customers.