97 Cavalier brake chattering at 80 km/hr or higher

I think it is time to find an accredited brake specialist . At the best with a hub it may be bad wheel bearings but I consider it a problem with the mechanics and their lack of commitment to fixing your problem

Sounds like you need to get your tyres balanced. If the vibration is when you don't touch the brakes only between the 80-100.
If its when you touch the brake pedal and the vibration occures, your disc brakes are warped, either machining or replacement.

What about the wheel bearings an what not? They been replaced?

if you adjust rear brakes that will also adjust parking brake

throttle cable

check wheel bearings , loose ball joints steering idler arm...

try the rear wheel hubs the noise will travel true the car making it sound like it up front

Sounds like your master cyl. is going bad.

The problem is the torque converter solenoid. I had it happen on my 94 Cavalier a few years back and was a cheap fix at the local car mechanic. What happens is the transmission warms up and hits a certain speed where the solenoid engages, but then it sticks and won't disengage until it cools down sufficiently. When it sticks, it causes the car to shake when slowing down and will snub out the engine if you come to a stop.

your probably feeling a rough idle of the engine. need a tune up?

in park the engine is not loaded down, just idling at a low rpm=rough
in drive with brake on you have put some load on motor also at low rpm=rough
in drive on the road engine is at higher rpm, = smoother

generally 4 cylinder motors idle a bit rough, especially if one spark plug is not firing right or fouled or one bad spark plug wire. tune up may fix it. if it is not stumbling real bad or stalling then you can live with it.