If you really want to recover the diamond, you'll have to call 911 and report it stolen. You will probably have to tell them your stepson stole it and pawned it, etc., to trace it to the new owner. Your stepson will be charged with a felony. The police may or may not be able to look through the pawn shop's records to find the buyer.
Even if you don't want to prosecute your stepson, you might still have to report the theft in order to recover from any insurance policy. An insurance adjuster may ask questions before processing the claim, and any answers you give insurance may be passed on to the police.
I do not envy your position. I don't think you can require the pawn shop to disclose its records to you without calling 911.