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I would try GWs to the car dealer and explain what happened. They may not do anything but its worth the shot.
Absolutely. Send a GW to your auto loan creditor and explain to them as you have here. You've nothing to lose.
Kids screw up. GW definitely.
What were the duration of lates? 30's 60's 90's???
EDIT:
I'm signing off now, so I won't see this for a day or so. I think that with your being caught up, on top of a letter of explanation, and another from the car lease people saying you're current, should suffice, and they'll probably turn a blind eye.