Be a man, tell your father what you have done, suffer the consequences. It's your fault, you pay. It's not right that your mom should be stressed about this, the truth will come out anytime. Sooner you solve this with your father, better for your ass,
Also, my second advice : if you can pay, a negociable amount (as somebody said that the debt collector got your skin for 30 bucks or so) then pay, just once. If you can't pay or negociate then just don't pay anything! Not even a single dollar. If you pay any amount of money then you give hope to that collector and they will try to squeeze you even more. They will even try to use this in a court as a fact that you-your family know and approve that you are in debt to them. The letters will continue to come, regardless of what you do.
Good luck and remember, this is not the worst that could have happened.