Do you really want to shut down the website? That could be a fatal blow to a growing business (if there are no revenues, then there is nothing for you to recover). What you want is a credible threat based on your legal rights. In business, the certainty of a negotiated settlement is often preferable to the expense and uncertainty of litigation. You need to consult with an attorney to determine if you have a credible case, and whether a take-down notice, litigation (e.g., a preliminary injunction), or something else is the best legal avenue for you to pursue.
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You will need to assemble all your documents and organize your emails and consult a business /IP litigator. Demand letters do not have the impact they used to years ago, but you can try.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
You may have a number of claims against your partners, although, from the facts that you presented, this is probably a more complicated matter than you might expect. First, if you applied for the copyright, most courts, including the 9th circuit (where California is located) allow you to file suit for copyright infringement now-you do not need to wait for the copyright to be issued. However, it is not clear that you actually own the copyright; from the facts you gave here, it may belong to the partnership you have with the others (no documents are required to establish a partnership, and from the facts given above, you have one). There are other, and probably better, claims that you can bring. However, you are in California, and you really need to seek advice from a sharp California litigator.
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I agree that demand letters typically are not worth the weight of the paper they are written on. In this situation, you will likely have to file a complaint and seek an injunction. You may also have grounds for a UDRP action which occurs through ICAAN and is a much faster way to address rogue websites. You will certainly have to consult with a knowledgeable lawyer familiar with intellectual property issues and litigation strategies.
This is not a legal opinion, and should not be relied upon as such.