Is this something that already happened or are you simply planning ahead? You do not have to answer questions and you can use that language. But why would you? It would only inflame the situation. It is not a crime to direct profanity to the police in your own home.
You lost control when you let the police in without a warrant.
When the police are in, there are few, if any, witnesses other than the police to what then happens and the police are free to use anything visible which is evidence of a crime. Temper tantrums and obscene outbursts will not cure those problems.
The foregoing is for general information purposes and does not establish an attorney-client relationship.
The NY "anti profanity" statute has been held to be unconstitutional so technically in it of itself with nothing more there is nothing illegal with being profane, certain,y in your own home. You certainly don't ever have to answer any questions the police ask of you (and I would never advise talking to the police without an attorney) and yes absent a warrant you are free to ask the police to leave your home at any time (though at this point they would probably conjure up some excuse that would allow them to stay). If this is a real scenario make sure you get an attorney ASAP.