I think the issue may well be in the ‘tone’ of your Email to them. It looks from the outside as if you are threatening the hotel as opposed to trying to alert them to an issue.
Perhaps a discreet phone call to the duty Manager might have had a better response.
You then go on to accuse them of being patronising, and infering that you are lying, (which I do not see in their responses to you) all the time taking an aggressive stance including the use of capitals which, in writing, is generally recognised as SHOUTING.
I have to confess to being unimpressed with their phrase about desk staff not being PA’s but other than that, I think its the tone of your note which is not professional at all (in my opinion, you did ask)