Peder

Im not aware how you build the rocket, but if you have used "docking" /ports/. Then you need to be aware that docking ports/modules as standard share fuel. So maybe the engines that first fire and burn, suck out all of the fuel from the top of the rocket. So when you try to fire the step 2, you are actual out of fuel... It is just a guess since we cannot see the rocket your build. ( right click the docking port and choose disable crossfeed ).

Im not 100% sure, but try to exit to the spaceport and then jump back into your space station. Normal that will stop wobbeling and make a station steady again. Maybe even try to exit the game and jump into your space station. Im not 100% sure if it also will stop spinning, but try. Or try to speed up things using the time acceleration function.