I've seen many situations where I've thought "that would have ended better if only they'd been prepared to act in a more mean way", but I can't think if I've ever thought "that would have ended better if meaner words had been used".

So it's OK to do the mean thing and tell someone who travelled to your party that they weren't invited and they can't come in if circumstances warrant, but you'll get the best results if you tell them so firmly but as nicely as possible.

I've mentioned my motto here before: as polite as possible, as rude as necessary.