"Does anyone know how to stop this unwanted turning?"
You will learn to control that and soon you will be able to paddle as long as you like on one side and still go straight.
The trick is to sink the rail on the same side as you paddle..Normal reaction is to sink the other.
Also get your left hand over the right rail of the board when paddling on the right side..and visa-versa.
Getting the paddle blade more under the board helps heaps.
One more thing..The paddle stroke..You will develope a stroke that keeps you going straighter.
It all takes time but you will get there..Jeez it's only been a couple of days..

btw..Paddling a few strikes one side and then swapping sides is not such a bad thing because it gives the tired muscles a rest.
DJ