I am a police officer. I can see this from both sides. Yes you were stupid and you realize it (somewhat) but part of remorse is making things right by fessing up and maybe doing some kind of community service to atleast heal some of your internal pain. When you say youre remorseful and then do something else stupid like lying to your old man to cover it's just wrong and a step in the wrong direction. Think about it this way.... You pretty much got away with this, no arrest... you fooled your dad ect. But now you may start to get feelings like you are invicible especially when your buddies are pressuring you to do something else stupid. Whether you tell your dad or not that is your choice. What you must do is take it as a life lesson and learn good and hard from it. Do some volunteering at MAAD or go to a AA open meeting. I would forget about the car and focus on proving yourself to well ummmm yourself. Grow up and realize that you dodged a bullet this time. You have so much time to go to bars and parties when youre 21 and not driving. Get serious and grow up. Dont listen to the BS that your a kid and have fun with no consequences. It's too early in the game to screw up. The mistakes you make now will follow you around for the rest of your life.
Take care and be safe