If he doesn't notice your vehicle disappearing while he writes the ticket, the policeman's probably not going to understand your explanation. Stick to the facts -- just not the obvious facts. Answer the questions, but give only the expected answers. Don't elaborate.
And don't count on the prince coming to your rescue. He's looking for a lady to fill the glass slipper in his hand, and you're only a barefooted peasant, aren't you?