No doubt there is an interest in a car-hop category. However, that should not deter you from the present process for the Sonics category. The interesting thing about a car-hop/drive-in category is to have a place to waymark non-chain car-hop/drive-ins. The way to do that is to establish both categories; Sonic and car-hop/drive-ins. Then, in the car-hop/drive-in one, suggest that if the place is a Sonic, just waymark it in the Sonic category. That way, the non-chain car-hop/drive-in category only has the interesting non-chain ones!
So, starting with the Sonic first is the best thing. Then the more unique category can be made.