wiggles

Hi Everyone, My dad nearly had an accident the other day because of some serious fault with this car :(. Basically when driving at speeds like 40, 60, 70, 80 and 100 the car starts the wiggle left to right then stops and when you put your foot down again it starts to wiggle again left to...

the circular base on my star wiggles if you ...well... wiggle it. I know it's got a spring mechanism underneath, but should the base wiggle a bit or should that be tight and just the middle bit ...wiggle. Equally non-technical answers appreciated :)