Why are the trucks getting stuck in front of my prison?

Solution 1:

For a delivery area to be considered valid - and thus a stop for the truck - it has to be connected to the curb of the road. (That is, one square to the left from the actual road.)

Your fenced-off delivery area is in a valid position and therefore the truck stops there to be unloaded. The workers, however, cannot access the truck, as the position next to the truck is blocked by the fence.

If you remove the fence, your truck should be accessible and unloaded appropriately.

Solution 2:

Also, check if aren't any small delivery areas. I mucked about with the different areas but a 3 tile big delivery area was still there. But it was filled up with random supplies so I didn't see the words and the driver couldn't unload. (Because the area was full.)