So perhaps this is what happened:
Your neighbor told this people that they need to stop parking there, and when they asked why, told them that you had said so.
So you should tell a that as far as you are concerned, they are welcome to park on the other side of the driveway which belongs to your neighbor. They certainly aren’t complaining about not having the right to park on your land (regardless of what it cost, I’m not sure why you would mention that).
If in fact you don’t want them parking on the other side, then that is why they are mad at you. It isn’t your land.