Your situation is frankly very fact intensive. If you are both co-authors then you both are permitted to exploit the material as you wish but you would owe the other an accounting and a cut of the proceeds. The fact that she is the only "author" noted on the US Copyright Registration is NOT disspositive of anything and further may present a dubious fact should she be found later by a court to have made that registation fraudulently.
The fact that you have a written agreement such as your LLC operating agreement can further limit the use of this material and it sounds like she may be violating that on its face among other aspects such as duty of loyalty and care to the business of which she is a member.
I would advise discussing your situation in much more detail with a lawyer in private so a best course of action can be determined.
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The operating agreement will likely control - the book will be an asset of the LLC that she alone cannot use for personal gain.
If this answer was helpful, please mark it as helpful or as a best answer. This answer is for general education purposes only. It neither creates an attorney-client relationship nor provides legal guidance or advice. The answer is based on the limited information provided and the answer might be different had additional information been provided. You should consult an attorney.
If you both contributed to the book and intended that your contribution be merged (which seems a logical assumption here), then the copyright is automatically co-owned by both of you under joint-ownership. As a joint owner you have a right to 50% of all proceeds from the book. This assumes there was no agreement specifically addressing ownership of the copyright.
This answer is not legal advice nor should it be construed as such. I always attempt to provide factual information relevant to a question, but, in the end no attorney can properly advise a potential client based on the limited facts that can possibly be disclosed in a format such as this one.
You may have a claim as a co-author of the book and co-owner of the copyright in the book, and that her copyright registration was fraudulently obtained, and therefore invalid. A co-owner is entitled to a pro-rata share of proceeds from the work, so you might have a claim to some of the income she makes from the book through her separate business.
The LLC may also have a claim to ownership of the copyright in the book, which would likely mean her use in a competing business is infringement unless authorized by your LLC (or an agent acting within his/her authority). That could get tricky if she has the authority to authorize such use (although it might be a breach of fiduciary duty).
All in all, this sounds like a case where you will need a copyright attorney to review factual details and relevant documents to get any sort of reliable answers to these questions, and advice as to which theory would be more advantageous to pursue.
I am an attorney, but I am not YOUR attorney. By providing free, generalized information, I am not entering into an attorney/client relationship with you, nor am I providing legal advice applicable to your particular needs.