I doubt you can get a full refund. First they will try to
rectify the engine problem. If there is no solution, they will only
replace the engine under warranty and not the whole car. Worst
case, they will buy back the car from you. Very unlikely that they
will do a one-to-one exchange for a vehicle, especially with a PI.
The trouble and cost of de-registering the current car just for
warranty and registering another one is not costworthy, even for
authorised agents.
Suggest you concentrate on getting them to have the engine
problem rectified first.