Rear tires shaking

Hi when I am driving at forty to forty five or faster and I hit a bump the rear end starts shaking, if I hit the brake it goes away. But everyone I hit a bump the rear end shakes. I tried letting go of the gas pedal no difference once I hit the brake it goes away. I have new shocks on but this has happened before I changed them out. I am not sure if the tires are unbalanced or if it is is the u joint. I hear a rattle when I accelerate but it is towards the front. my friend is a mechanic and he said the driveshaft is trying to set in place. It gets worse every time I drive it. Also, in the front end the steering is terrible I know the steering gear needs to be replaced but it pulls hard to the left. I sometimes get a shake in the front end. I have not looked at the ball joints lately. I looked at the tie rods they are nice and tight and have no play in it. My friend said if I change the steering gear I might as well change the tie rods the upper and lower ball joints. So he can align it after he is done. There is a lot of play in the steering wheel and the gear box is leaking.