A successful grapple moves the victim to a square adjacent to the grappler. It also prevents the victim from moving, until he either breaks the grapple or reverses it (at which point a successful attempt to maintain the grapple in subsequent rounds lets him move half speed).
These would suggest that Monster A's successful grapple prevents PC B from simply riding away on his mount, and that directly implies that PC B cannot simply remain in the saddle or order his mount to move him away.
As for the equestrian belt, there are times when two rules are in conflict. In this case, if the GM rules the grapple the same way I just did, then we have one rule automatically taking the victim out of the saddle and one rule automatically keeping him there. Conflict.
GM's judgment.
One thing that might guide this judgment is to ask how the belt works. Does it literally glue the user to his saddle, or extend some kind of "seat belt" that straps the rider into the saddle so he can't be removed? Maybe, but that's reading a bit more into the belt than the actual item has written. It's probably more like the belt gives the rider the skill to be a super-awesome rider and never fail these skill rolls, but it still requires the rider to be ABLE to make the skill rolls in the first place. If this is the assumption, then being yanked out of the saddle by a combat maneuver would mean the rider is no longer able to make riding skill checks because he isn't riding anymore, so the belt wouldn't help him after the grapple is successful.
Stay in saddle checks are for if your mount rears, bolts unexpectedly or you take damage while riding.
I would rule the grapple pulls you off the mount, adjacent to the grappling creature. No bonus for being mounted.
I am hesitate to throw a wrench into this, but I think someone else would if I didn't. What if you've a saddle specifically designed to keep you in the seat? They make saddles for flying animals that will keep you planted to the seat even if your mount were to fly upside down. Seems like there out to be a bonus against. Heck, if a character really wanted to stay seated they may even use sovereign glue. At the very least they should be able to tie themselves into the saddle such that they can't be removed (at least by a tackle or grapple).
And I honestly think that any character that has focused on building themself as a mounted warrior specifically would probably take such precaution against being unseated by a grapple, or a bullrush or anything of the like.
I am hesitate to throw a wrench into this, but I think someone else would if I didn't. What if you've a saddle specifically designed to keep you in the seat? They make saddles for flying animals that will keep you planted to the seat even if your mount were to fly upside down. Seems like there out to be a bonus against. Heck, if a character really wanted to stay seated they may even use sovereign glue. At the very least they should be able to tie themselves into the saddle such that they can't be removed (at least by a tackle or grapple).
And I honestly think that any character that has focused on building themself as a mounted warrior specifically would probably take such precaution against being unseated by a grapple, or a bullrush or anything of the like.
I believe the saddle you are referring to is a military saddle.
"Saddle, Military: This saddle braces the rider, providing a +2 circumstance bonus on Ride checks related to staying in the saddle. If you're knocked unconscious while in a military saddle, you have a 75% chance to stay in the saddle."Unfortunately, that is for a ride check to stay in the saddle, not a bonus to your CMD.
Sovereign glue would be overkill, because you can't separate the surfaces without universal solvent. Makes using the bathroom hard. If that was the case, I would rule that the PC was grappled, but still mounted, and since they share squares with their mount, and the PC is unable to move, the mount would also be unable to move. I'd rule the same way for any "can't be removed from saddle" strategies. Not RAW, but the situation isn't exactly covered RAW.
In the real world, nobody wants to be tied to their saddle because if that horse stumbles and rolls, you get crushed. Possibly killed, probably broken bones, almost certainly very injured and sore. To survive a falling horse (or motorcycle) with minimum injury, being thrown clear of the heavy mount is necessary.
Of course, in the real world we don't have riders with more HP than a locomotive, so maybe that's a moot point.
Frankly, if someone wanted to be perma-saddled by gluing/tying/belting themselves to their mount, I would just apply the grapple to the mount's CMD instead, and say that both the rider and the mount get grappled simultaneously, since they're essentially one inseparable creature at this point.
I'd also look for ways for them to be knocked off a cliff or to ride into other dangerous situations, say, with the mount being Feared or Controlled, and the rider would have to suffer the consequences of being attached to his saddle, not to mention the consequences when that mount is tripped, paralyzed, killed, etc, and the rider winds up getting crushed underneath the falling mount - far more survivable for a Pathfinder hero, but still damage and inconvenience that wouldn't exist if he didn't attach himself to his mount.
All I'm saying is I think in a world with magic they're has to be a way for riders to be reasonably protected against being removed from their saddle. I do agree that the rules don't cover this well and I'm not sure how to adjudicate such things.
I would actually be interested in seeing specific rules from Paizo developed to handle these situations.