Need help isolating source of interference
At the very least, you're going to have to put some capacitors across the motor terminals, AND from each motor terminal to its metal case. Even the cheapest toys have such capacitors, or they would get in trouble with the FCC pretty quick. In addition, you're going to have to consider the fundamental frequency of the PWM signals you're feeding the H-bridge, along with all its harmonics. These harmonics will vary from "all odd" harmonics with a 50% duty cycle, to a complex blend of even and odd harmonics near the very low and high duty cycles. Chances are one of these harmonics is at or very close to the frequency your RFID reader is looking for.