Thank you for your question. Please permit me to assist you with your concerns.
My apologies to you for being in this situation. I will directly answer your questions and point out concerns, but if the answer is not as you hoped, please do not blame the messenger.
Do I have a case against the law office that falsely sent me papers only to hand it to her for her own purpose.
The answer is 'no'. Anything attorneys draft is for their client, and it does not mean that the document will actually be used. The attorneys are not responsible for the filing unless they were hired to file it as well. For example if you hire me to draft a contract for you to use to buy a bakery next door, which I draft for you, the baker cannot sue me if you end up never using that contract (as I did not represent the baker, he has no basis to sue me, or demand that the agreement be utilized).
What you CAN do is file on your own. You can check the courthouse and see if anything was actually filed--contact the clerk, give them your last name, and see if anything is on the docket. If not, and it likely isn't there because most filings are removed after 6 months of inactivity, you can simply draft your own documentation and file on your own. I realize that this is not potentially ideal, but if you want to be divorced and she isn't filing the documentation, you can file yourself and then if she refuses to sign, you can push for a default divorce instead. And you can file in your own home state and not where she resides because either state is a valid location for pursuing divorce.