Since it happens when your braking, I would still believe that the brakes are the source. A shaking when braking almost always points to a brake rotor or brake drum that is out of shape. If the steering wheel wobbles during the shaking, it is from the front. Also, drive the car for 5-10 minutes, city driving, and then feel each rim to see if one is particularily hotter. (Expect both fronts to be hotter than rear ones)If it is the front, and the rotors where replaced, I would remove the rotors, return them to the parts store as defective, and put the second set on. when replacing them, be sure there the hub surface is clean and flat. Re-check the caliper slide surfaces that the are clean, not worn and coated with high temp caliper grease-(not anti-seize). Be sure the caliper piston is returning and is moving back and forth as it should be able to do. IF the problem is from the rear, replace either the drums and adjust the shoes if it has them or replace rear pads and rotors.
It must be the rear brakes at fault.
Try having your tires balanced and rotated. I used to have a car that would shake very bad when applying the brakes and I did everything you did. Then a guy told me to have my tires balanced and rotated and it fixed it until the tires became unbalanced again.
you have out of round brake rotors, they can be replaced or machined if they are thick enough, the front pads should be replaced or placed on sand paper on a flat suface to remove the glazing so they will seat properly to freshly machined surface
pull the fuse
Applying the brakes.
This could be for a few reasons, but if they are getting hot without you applying them, I would suggest that they are sticking and causing the pads to rub on the discs, or if they are drum brakes, the shoes on the drums. If they are only getting hot as a result of using the brakes, I would suggest checking that the brakes are balanced properly, and that the front brakes are not doing all of the work/ or that the back brakes are working at all.
Warpped rotor. rotors are warped have them checked and turned or replaced. they should be turned after every brake change
Using brakes slows your speed.
check for loose front end parts. check cv axles.--Also check motor mounts and transaxle mount.
brakes, or no sun
Brake rotors or drums need to be machined or replaced. If it causes steering wheel shaking, check front brakes. If happens when applying parking brake look to rear brake problem.
Yes, that will work.