I would have said it was the game, but you have trouble shot that issue away. And you say that you switched pedals and still get the problem?
Seems to me it could be one of a few things. Are the pedals made by the same company? In my experience with gaming peripherals, sometimes they are not constructed with the highest quality standards. (it could be a common structural weakness for that company. Eg: two bad pedal sets)
Something you can try if you feel capable and comfortable doing so.
It is sounding to me like there is just a loose connection in the pedal controls, due to possible manufacturing or normal wear and tear, issues.
(Use caution here, you know yourself better than I do. Only you can say if you can do this and remain safe. If you have a bit of experience taking electronics apart and then having power flow through them for "diagnostic" purposes. I think you should be fine. As you shouldn't really have to cut or modify anything)
So carefully take apart the pedal unit. So as that the "shell" is off. And then fiddle with the variables. (Try putting the accelerator to "full on" and then back it down to "full off" and see if you still get the braking response in game. If the problem is what I think it is, it will likely work fine. If not the next thing to try is to see if you can "induce the issue" that is to say, get the brake/reverse function into its malfunctioning "always on" state. (So in game the car brakes and then reverses.) then GENTLY fiddle with the wiring in and around the brake pedal control thingy. As you watch the brake/reverse lights on the car. Using this fiddle method of trouble shooting, you may find the manufacturing error or wear and tear damage.
This is a little convoluted and I apologize, I don't have experience with racing wheel rigs, much less your model of racing wheel set up. But I have taken apart many differing electronic devices, and many times the "fix" is a piece of tape that prevents a wire from jiggling.
So, if you have it apart and it functions fine, you may need to gently modify the shell so that the brake pedal can go all the way out to "full off". If you have it apart and can induce the issue but the fiddling doesn't help. Or the fiddling led you to a partially connected wire, you may then want to contact a local electrician. Or look to see if there is an electronics repair something or another in your local area.