BMW Repair: stalling after a hard brake, excessive air, stickshift

Question
my car is 525i 1992 timeing chain car. the is after i make a hard brake,actually a quick hard brake and then press the gas the transmission has a delay. the car is an automatic.ic car is fine when i do a rolling stop, or a slow complete stop. but when i do speed racer stop it sorta stall like in a stickshift. i dont speed,nor mash the gas at red lights. if there is any info please let me know , thanks  

Answer
i believe the delay is lessened if it's in manual or sport mode, economy has a different shifting stratagy.
most likely, the brake booster has a hole in it, the reason the engine stalls out is because the diaphram is letting excessive air into the intake leaning it out and causeing it to stall. get up to speed, put the car in neutral and mash the brake, does the engine die or bog down significantly? it could also have something to do with the transmission computer thinking it's in manual mode or a clutch or solenoid sticking,  should that be the case the engine code should tell you whats up with the transmission.
get it plugged in to read the vacuum readings while you are performing the sudden stop. What happins if you stop the car with the mecnanical linkage (e-brake) if this also causes the engine to bog down the problem is in the transmission.
-cheers