Yes you could use drill motors, but they are quite bulky and probably awkward to mount. The stock motor is probably small and running at 6 volts(or less), which might be too low for the drill motor. You would probably be better off with a 6 volt micro metal gear motor. You can buy mounts for them as well. Another option would be the Tamiya gear box:
https://www.pololu.com/category/34/t...-and-gearboxes. They are another popular option for converting toys into R/C. As for forward and reverse, if the setup you have now has forward and reverse, then the new motors should be the same. You may run into issues though when the new motors draw too much power, and burn up the electronics in the toy.