You need to hire a Patent and Trademark attorney and sue the complaining company for interfering with your Trademark rights. You attorney will request a preliminary injunction against the company commanding them to cease and desist filing false claims with Amazon and to withdraw all previously filed claims.
Once you have that you will submit a copy to Amazon and they should restore your account.
Under Trademark and Patent Law you are entitled to recover triple damages (and attorney fees) from the offending company. But it is up to you to enforce your rights, not Amazon.
Amazon is only responding to what appears to be a valid infringement claim. Amazon is not a Federal Court and cannot make a determination whether a claim is valid or not. But once you file a lawsuit to enforce your rights Amazon will provide you with the papers the company filed which had to be sworn under the penalty of perjury.
I am not an attorney but had a similar situation with NYC and another online site. I took NYC to Court (spent $40,000.00 in legal fees) and won. NYC had to recall every false claim they made against me notifying the other site of their lies.
One other thing - you need to file your trademark registrations with Amazon and Brand your products.