179,000 miles on 2005 Mercury Mountaineer. Started shuddering when braking and was getting progressively worse. Husband replaced the rear rotors and brake pads with new.

check you rotors possible slight warp

If it is the idler pulley for the accessory belt, it would make the sound at all times the engine is running, not just under acceleration. I would look to the wheel bearing or the brakes on that corner of the vehicle.

Warped front rotors,replace or machine flat if they aren't worn below spec.Most parts shops can give you the specs for the rotors.

check the parking braske that is inside the rear rotor. the back brakes has brake pads and a parking brake shoe

Take a look at all the rotors now since you have replaced them. If you notice any unusal wear on one or more rotors, then i would say either the rotor is defective or the brake caliper is at fault. Even with new rotors it does not mean that they are perfect. They may be out of round or they was cut wrong. The problem would even get worse with a caliper piston trying to stick from time to time. Take a little time and inspect each roter inside and out for any kind of unusal wear. Hope this will help you.

you probably should change the transmission fluid and filter with that many miles on it.

you don't the rotor should just come off if not there should be an adjuster wheel in the backing plate

This can be from warped rotors. Also try cleaning rear abs sensors. What happens in rear is brake dust does not have momentum at low speeds to fan out away from wheel sensors. Loose debris falls into abs sensors and makes abs activate. Big culprit in rear is emergency brake linings separate and get crushed then foul sensors.

The steering wheel shutters? How long has it been doing it?

Did you buy factory pads or get cheap aftermarket pads? If aftermarket did you get the ceramic? The cheap aftermarket ones tend to squeal pretty bad. Like the last comment on here, you should have your rotors turned whenever you change the pads.