Back end shakes

No ball joints in the back, but you're right about the tires. What you're describing is exactly what a broken belt will cause. A tire and alignment shop can inspect the tires and show you how the tread is squirming sideways as it goes around. This is much more common with Uniroyal tires and to some extent B.F. Goodrich tires, but it can happen to any brand. GM has a real lot of trouble because many of their cars come from the factory with those two brands. I've found it quite common for Goodyear tires to develop broken belts right at the time they should be replaced for worn out tread, like you'll find on my Grand Caravan all the time!

Caradiodoc