Quote from BeckEach character has their own car. So that will always be parked outside their house.
I'm not sure how the game decides what to impound or not. Does it only impound one car?
Well, while playing as Franklin yesterday, I have my own garage, and if I get in the garage while on a Car or a Bike it stores that vehicle inside the garage. But I still think you have your own personal car, at all times. I have no idea how to change it tho, or if it's even possible. It's really confusing.
Also, where can you customize your car again? I know it's in Los Santos Customs, but where is that, and how do I do it?