the motor operating voltage is 6V .. you can safely run it on 12V if you do not exceed 50% pwm. Also, if you limit the current, you can run it on 12V without any problem.
With regards to mosfets, irf530 is not 6V .. IIRC those are 100V mosfets and need 10-20V to open fully, irf9630 is 200V mosfet that need -10V to open ... so your major problem is that you are opening them with 6V so you do not get them open, and the Rds is too high. Using the driver like TC4428A or similar you can take digital input (0/5V) to open the mosfets. If your input is 6V, put a resistor and a zener and clamp it to 5V or check the datasheet for the driver, many of them are up to 10V tolerant