You may need legal advice, just a few hints: According to Wikipedia http://en.wikipedia.org/wiki/Customs_duties_in_the_United_States goods must be declared within 15 days of arrival, so you might be fine. I personally would think that if you aren't caught but declare things yourself as soon as possible, you might be fine, but as I said, get legal advice.
You will have to pay some import duty. I would declare the facts that I know (that I bought what was I thought was a $6,200 ring, paid $6,200, and they claim it is $9,700) and let the customs people decide.
The other problem is the $3,500. Again, you might want legal advice. I would base my decisions on the facts that (1) you had no intention of buying a $9700 ring, (2) you left the shop with what you thought was a $6200 ring that you paid for, (3) it was their mistake, (4) jewellery has high profit margins, so they will survive their loss, (5) they are trying to force you to buy goods that you don't want by unethical means (they advised you not to declare the ring at customs and used this to try to blackmail you), and (6) there's probably not much they can do.
- You had no intention of buying a $9700 ring
- You left the shop with what you thought was a $6200 ring that you paid for
- It was their mistake
- Jewellery has high profit margins, so they will survive their loss
- They are trying to force you to buy goods that you don't want by unethical means (they advised you not to declare the ring at customs and used this to try to blackmail you)
- there's probably not much they can do
