[Kevin Sevcik]

The problem is that you're trying to force the wheels to slide sideways because you're using 4 wheel drive. I'm guessing your effective wheelbase is longer in the forward backward direction than in the left right directions. If you think about it, this forces the wheels to slide side to side.
To use an extreme example, imagine trying to make a bicycle turn in place. The wheels have to slip side to side and their turning forwards doesn't help at all.
Now imagine a segway, it turns on a dime with no problem, and the wheels don't have to slip slide to side.

So you have a few solutions, but this late in the game you have to decide what's practical:
1. go two wheel drive with casters or skid plates. (I;m not trying to start the usual holy way about 2 vs. 4-wheel, I swear).
2. make your wheelbase more segway-like by moving the wheels closer together so the wheelbase is wider than it is narrow. Team 57 did this this year and our robot turns MUCH better.
3. bald one pair of tires so it will slip side to side.
4. go 6-wheel drive. the middle pair will force the robot to turn since it will be applying force directly to turn the robot like the segway wheels.
5. Make Omni-Wheels for one pair of wheels.

Keep in mind this is just from my experience with my team's robot, though. I've seen other teams make 4-WD robots that turn with no problems, and I've no clue how they did it.