Take your other car. If you are not comfortable parking at a place — and I totally understand that — you won’t be relaxed and won’t have your mind in the dinner conversation with your girl. That she says “it’s only a car” means she just does not understand and won’t understand your uneasy feeling. She’ll pick up on your uneasy mood and take it all wrong. So, in this case leave the G and take a less flashy car, enjoy your date, and take your other girlfriend— the G — out for breakfast.