In most states, there are certain types of agreements that must be in writing to be enforceable. Typically, any agreement that is worth more than $500 must be in writing. So, it will be hard for you to get the $2,000. However, you are entitled to get the wedding set back.
To do this, due to the small amount, representing yourself in small claims may be your best bet. Here is a link to more information on small claims proceedings in your area.
Prior to filing any action, you may want to send the girlfriend a certified letter setting for the facts and your demand for return of the wedding set. If she doesn’t respond, that will help build your case with the judge. If she does respond, then you will at least know where she stands.
Although there may be some variation from state to state, the general rule is that an engagement ring is a conditional gift, conditional on the wedding taking place. Your future brother-in-law is therefore entitled to to have the rings returned. The fact that an engagement and wedding ring were given should make no difference.
Historically, the law awarded the ring(s) to the person without fault, the one who did not break off the engagement. However, the modern rule makes the gift conditional.
Your future brother-in-law has the right to recover the rings from the girlfriend. He should then return them to you.
As to the contractual aspects of payment for the rings, the oral agreement may be enforceable, though proving the facts is always a challenge.