are all your tires worn evenly? the same size? etc?

are the brake pads evenly worn or the even rotors drums? are the calipers extended the same amount?

car stops ok? is the brake fluid low?

the shudder should only occur while braking, is that the case? i "think" the light should diagnose the problem if you can it, but i really have no idea on your car, is it obd2 compliant? i am willing to bet with the miles and the problems i have heard about, it either your rear brakes arent stopping as well as your front (and hanging up).. or the calipers are extended and the fluid is low after/during you pressing the pedal..