Welcome to the Forum, mysterious 21!
I've encountered the same problem. Technically, if the parking space fits on the lot, then the car should fit just fine. I think it's a bug that's not letting it happen, which EA will probably fix. In the meantime, try placing the car with Move Objects On. To do this, you need to open the cheat console by pressing ctrl-shift-c. You can tell the cheat console has opened because your screen will get a bit darker and you'll be able to type. Type exactly this: "moveobjects on" without the quote marks, then press enter. When finished, repeat the process with "moveobjects off" to return to normal gameplay. This function lets you place objects anywhere on the lot and is usually used to make unusual decorating items, but I think it will also let you place the car on the parking space. Let us know if this works for you.