Sounds like warped brake rotors to me. If you overheat the brakes riding them down long hills that can do it. Maybe the front rotors need to be checked too. When they warp the steering wheel shakes a lot every time you brake.

Recheck lugnuts first. Then brake hard parts for warp or fat/skinny.

You can spin the wheels in the air to eliminate them.

Sounds like you may have rear disc brakes, this means check the parking brake and the calipers. you dont want to repeat the problem, and axle flange/hub runout can be checked with a dial indicator.

i would have the suspension checked and new brakes are cheap.

it will probably be the discs or pads might want to check it out

alright so I drive a 2001 impala and everytime im about to come to a stop and apply the brakes I feel my back tires shake and eventually makes my whole car shake, could my brakes be going bad already, or does it need some type of alignment?