From what I have researched it seems we are liable for any accidents that may occur if they have any sort of accident on our driveway.
Already your research is flawed. You're not automatically liable just because an accident happens. A person seeking damages would have to prove you were negligent.

From research it seems they don't have a case for prescriptive easement since they have always had permission to use our driveway. Nothing was ever written down but we gave them a verbal okay when we bought the house. Nothing open and hostile plus we all use the driveway - it's not just for them. It also seems their parents created an easement by necessity when the land was divided upon their death. Our neighbors could run a driveway across their sibling's land to connect to the public road. They never did this because it was easier to just use the driveway that goes over our land and it didn't require a cash outlay!

Does my conclusion seem reasonable?
Only if your "research" came from a real estate attorney who knows easement law, and not from a variety of potentially inaccurate internet sources.

I suggest you hire a real estate attorney to advise you before you make a decision that could get you sued.