I choose to believe that a cop has the right to bring someone in for further questioning under the charge of disorderly conduct when they refuse to control their behavior after being asked to calm down.

Neither your choice OR belief have anything to do with the rights or responsibilities of the officers, save that if you choose to hold to that belief when it fails to reflect reality, that is... a bit nuts.

If you're saying that, to the best of your understanding, this is how the law works, that's one thing. It might be better if you provided some statute or case law that supported this understanding, though.