Engine troubles! please help!

Please clarify...when stopping, does the alternator go to full discharge and then the engine start to stumble? What happens when you first start the car...does it run okay when it's not in gear and idling?

If I'm understanding the symptoms correctly, it sounds like you have a serious electrical short that happens when you decelerate or hit the brakes, and is bad enough to deprive the engine of adequate voltage to keep running.

If it was a fuel problem that was causing the engine to stumble, the alternator needle shouldn't be reading negative if the engine was still running, and even if the engine dies, it shouldn't show a strong discharge unless every accessory was running.

Just curious...did you recently install a monster sound system?