I would check for a vacuum leak first, then move on to the sensors. Sometimes a faulty MAF/MAP sensor will cause the engine to stumble while braking because the as the engine load changes, the faulty sensors don't allow the computer to react fast enough and the air/fuel ratio becomes overly rich for those few seconds and the engine stalls.
Don't just begin replacing parts. This will be expensive. You should test them properly first, and through the process of elimination, you'll find your problem.