Agree, agree and agree. Your sister needs to know what she did is no acceptable and she needs to pay you back most definitely no matter how long it takes. It also show she's not close to being responsible enough to actually have a license. Turning her into the police would scare the crap out of her but would cost your mother a lot of money in the long run. So I would NOT suggest turning her in. I would however not allow her to get her license until she was 18 but even then if she lives in your moms house and/or drives someone else's car your mother and/or registered car owner could still be held legally responsible.
With regards to the neighbor. If there isn't any damage to his house with the exception of the lawn being torn up, I don't see him putting out the money for a lawyer to sue you. He may be the one to call the police and make a stink and you'll probably have to fix his lawn. If I were you I'd offer to fix the lawn because as the registered owner of the car you would be held responsible along side your mother.
I'm amazed that your sister would think for a second it was okay to drive your car period. I have two daughters and neither of them would have ever tried something like that. Don't get me wrong, we've had our issues but they both would have been way to afraid of what psycho-mom's punishment would have been. I think that makes me the meanie!!!
But . . .Jay_Bunny, if you think you've got bad karma you'll have bad karma. The positive is she nor anyone else was hurt. Lesson learned, unfortunately on your dime.