There is a big chance that the brakes are not in good condition. You have to check the brake pads and discs. The other reason could be that your car's bushings need replacement. Also, the steering might not be properly aligned. Your tires needs balancing too. Or, your car may need new set of tires.
Excessive vibration usually means your rotors (the disc part of the brakes) are warped. The uneven surface causes the calipers and wheels to vibrate under hard braking.
Your brake disc rotors are warped, causing brake pads to oscillate back and forth while braking. This is felt as vibration through steering wheel and chassis.
This is a very common symptoms of warped rotors. When brake rotor get very hot sometimes the begin to warp. This warping can cause pedal surge or a shudder during braking. This could also be related to a bad alignment or loose or broken suspension components.
The most common cause of a car bouncing around when braking, though by no means not the only cause, is warped rotors and / or drums. You could try hand braking, though you should have this problem checked.