Originally Posted by JARblue

Yeah, so what has likely happened is your brakes were already pretty warm/hot when you had to brake suddenly. The cause of the shaking you now feel is when you stopped completely with those hot pads pressed firmly to those hot rotors. The pads continued to deposit pad material in that one location, leaving a high point on the rotor that is now noticeable under braking. You can try re-bedding the pads and see if that helps. Or have a brake shop turn them like I mentioned earlier.

To avoid this happening in the future, do your best to avoid stopping completely and holding the brakes down when your pads and rotors and rotors are hot (i.e. after any heavy braking). When I hit a yellow light that I stop for suddenly, I will often sit in N if the ground is level enough. Alternately, I put it in N and engage the e-brake just lightly enough to hold the car (you will have to do this in most cases in an AT). I make sure to tap the brakes a few times when cars are approaching from behind just to let them know that I am actually stopped.