Hi Techniix,
I don't post here a lot but your post was extremely unsettling for me personally and I wanted to offer my sympathy and suggestions.
1.). You shouldn't panic because your wife's status is not related to your possession of the physical green card. As long as she properly filed the I-751 and it is still pending, your wife is in status. The only issue is that you do not have evidence of this status and cannot (or should not) travel outside the US without the physical green card (the extension letter is not sufficient by itself). However for most practical purposes, inside the US, a state ID is sufficient. And as others have mentioned, your wife has the right to get a temporary one year I-551 stamp at a USCIS office. Google Infopass appointment to learn more about how to make this appoint. Also see: https://www.uscis.gov/i-9-central/temporary-i-551-stamps-and-mrivs
2.). Your wife's green card was not her property. It was property of the federal government, and destruction of federal property by an agent of the state is a serious crime. You can see, e.g., here: https://www.law.cornell.edu/uscode/text/18/1597. If you want to pursue this issue further, you can file a police report stating what happened. You can also seek a lawyer and get a consultation. To be clear, this is not an immigration issue but a criminal issue, and you do not need to seek an "immigrant" lawyer just because your wife is a permanent resident. She has the same basic rights as any citizen, with the obvious exceptions (like the right to vote).
After filling a police report and consulting with a lawyer, you can file a formal complaint with your state's DMV. Every state is different but if you Google you can quickly find how they process such complaints. For example, in Texas the page looks like this: https://www.dps.texas.gov/section/office-inspector-general
This process may take you some time and it is up to you how far you want to pursue the issue, but one can imagine how this DMV has treated other immigrants before you (and will treat others after you). Following through on this issue in the best case will force them to train their employees properly, and at the very least not break federal law.
Best wishes.