We are disappointed with your comment. You are right when you say that we did not agree to extend your stay, but it is not fair what you are doing. Our business is accommodation, and if possible, there is no problem in offering late check out, with or without cost. But if the hotel is full, there is no reason to do that. Do you agree to receive your room later than check-in time, when your child needs to take a nap, because the previous guest also had a child who needed a nap? We all know your answer.
It's not fair because we offered you to stay 1 more hour for free. And it's not fair at all, because you don't mention that we don't apply cancellation policies for your mistaken double booking, leaving a room unsold, and unpaid, because you made a mistake.
Nothing to say about calling the police, I prefer to think that your mother did not understand me when I spoke to her.
You actually seemed more understanding when we were talking about this and we offered to stay, and you accepted, in a quiet area of the hotel. But it seems I was totally wrong.