OK how the cars actually move is off topic from what you asked. Here's a suggestion with a could of options
Make a 1hu thin, invisible func_door over your road area. You could make the road itself a func_door, but you'd need to put a world brush under it so that the world is still sealed. In either case, you don't need the door to open or close at all, it just has to be there. Stickies can't stick to doors so they will slide about until they touch something they can stick to.
From here you have some options as to how you direct the stickies to move:
- You could make the door slightly higher on one side so that the stickies roll 'downhill'
- You could use a thin trigger_push brush over the road to move any stickies to one side. Just make sure you diable the 'Clients' flag so players aren't effected.
- Parent a point_push on the front bumper of each car. Disable the 'Push Players' flag and enable the 'No Falloff' flag. Set the range to a little further ahead where the cat meets the road. This won't move any stickies that have stuck the floor, but will move any that have not stuck to anything yet.
I was also going to suggest using trigger_remove brushes over your cars, but I could not get them to remove stickies at all, even with different filters attached. I don't know if someone else has made that work, but I haven't.