In general d.c. motors tend to run faster in one direction than the other, and since your drills are most likely mounted opposite ways round to each other, thisll cause your robot to veer slightly when travelling in a straight line. When you put your robot in reverse, is it the other motor that runs faster this time?

The sensitivity issue (assuming youre using a mixer) can usually be eliminated by adjusting the trims along the axes of the joystick.

Make sure your robot is set up with it facing forwards with you behind it (so that youre facing forwards too)
Push forward slowly, find out which wheel it is that starts spinning first, then move the trim (the one that runs along the bottom of the joystick I think it is) by one notch in the direction of the wheel that doesnt start spinning first - i.e. if the left wheel, as you look at your robot, starts spinning first then move the trim one notch to the right.

Push forward slowly again on your transmitter and hopefully the second wheel should turn after the first wheel starts, but more quickly than it did before. Keep repeating the process until both wheels turn at the same time when you press forwards (you might not be able to eliminate the delay entirely, but adjusting the trims should get it pretty close to both wheels start almost together)

Hope that helps, if Ive explained it in an understandable manner - it looks like gobbledegook to me when I re-read it