Right, but if I'm turning down an invitation, then obviously I don't have one of those options available to me.
Honestly, I wouldn't leave my dog with a stranger. I leave her with my adult children, and one friend. But it's my dog, so the responsibility lays with me.
Again, anyone trying to insist I care for my dog in the way they want, for their convenience is downright rude. I will care for my dog how I see fit, and frankly, I know what is best for her. Stop offering unsolicited opinions on how I care for my dog. It's disrespectful and rude.
If someone doesn't want my dog in their house I always respect that. I don't start trying to tell them they're living their life wrong, they should let my dog come, they should get a dog or any other nonsense. I respect that they know best for themselves.
In return, I expect that when I say that I can't come for reasons of dog care, then people don't rudely start trying to tell me what I should be doing with my dog. That they show me the same respect as I've show them that I know best for myself.
As I've said, I would always offer to host myself, or meet in another dog friendly venue. If the other people are so inflexible that they won't consider these options that's on them. They are the selfish, demanding and inflexible ones. I make no demands at all. I'll simply not come if my responsibility to my dog means that I'm unable to. It's just part of being a responsible pet owner.