Just to add that I agree with everyone on the rear tyre being the aquaplaning culprit, but all this huge instability is not only from being driven under power from the rear, but the car is also phenomenally unstable if the rear loses traction under lift-off engine braking. I had a monster of a moment last year when lifting off at about 30mph down a mud and leaf-mulch covered lane where the centre of the road was covered in thick clag. The car tried to swap ends like a b4stard with nothing more than a gentle lift..... Took a decent few handfuls of oppo to get it back in shape.
So over-riding rule is to be very wary of sudden changes of grip with respect to the rear wheel. Slow spin turns and all that mucking about is fine, but higher speed stuff needs careful management, for sure.
One fix would be to put a sticky motorcycle tyre on the back instead of the fat car tyre, much as those early 2- and 3-speeders have when racing and sprinting etc. A nice narrow, rounded profile which wouldn't suffer anything like as badly in big wet.
