Sekondly, i presume GSX should NOT generate the "set P-Brake command" when it's already done (as shown on the jpeg).
As I've said, GSX doesn't generate *any* command for you, under any situation. It only gives you alerts depending on your existing FSX variables, regardless how they ended up being in that state.
When using CH or Saitek pedals they (for many users) generate "noise" wich lead to a more or less permanent red flag (Differential Brake/Brake) in the lower left corner of your screen. Using Fsuipc to setup the devices is not recommanded flying PMDG.
So, according to your report, the real cause of the problem is that your uncalibrated rudder pedals ( the axis that controls progressive braking ) is constantly sending random brake commands, and this results in FSX turning OFF the *Parking* Brake, which is what normally happens with you press the dot key on the keyboard and the parking brake is engaged, which results the parking brake to disengage, if only for a brief moment. Perhaps the PMDG airplane is checking this, and send the opposite command back, if it thinks the parking brakes *should* be engaged. But the FSX variable changed, if only for a brief time, so GSX reacts to it.
I'm sorry, but there's no other proper way to fix this, other than calibrating your axes correctly, possibly using FSUIPC if you can't in any other ways.
a solution could therefore be to find a way to silence the P-brake command in GSX, even the core problem is not coursed by GSX.
This would be the worse solution. Regardless if GSX is being silenced or not, your internal FSX variable related to parking brakes is STILL changing!
Ignoring this is a mistake, because it would surely cause other issues in the simulation (the airplane IS braking constantly, what about if there was some kind of side-effect in added wear of some of the systems ? ). In fact, you should be grateful that GSX has exposed you to this problem, so you can fix it in the proper way, which is of course is acting on proper joystick calibration, not just ignoring it.