Is it more the braking, or more the shifting that causes the car to stall? If you have a vacuum leak in or around the brake booster this can cause the car to stall. When you put your car in park, obviously there will be a "shift" in the position of the transmission (sorry, just couldn't pass up that play on words) and the engine. If you have a loose wire, for example on the crank sensor which attaches to the transmission, it may wiggle and break the circuit. If you sit at idle, in drive, with your foot on and off of the brake...does your applying the brakes affect the idle? If you pull the emergency brake (make sure it holds) and don't use the brake pedal, can you shift the car into reverse (I'd say park, but I don't think you can because of the shift lock release) without it stalling? Play with it a bit and see what affects the stall more readily...the brake, or the movement of the drivetrain.

Chris