I think guessers agonise over HOW to say "No" in contexts like this, and what it says about them as people.

"Can my family and I stay for two weeks?".

Then:

"No." (looks cold and heartless; do I want to project cold and heartless? Will they hate me?).

"I'm so sorry but I'm not able to. The house is a mess and it's really small" (performative, hand-wringing reluctance; we both know I'm lying).

"I just don't like to share my environment" (most truthful; might look petty to those who don't understand the need for privacy to that degree).

All this rings true, which brings me to this question: are Guessers just a bunch of Overthinkers?

They are, yes

Having said that, I have become a lot better at being direct these past few years, so I'd likely just say "I'm not able to, sorry. I can recommend some good hotels though".