YANBU.
The way I see it, she has 3 options:
1: She brings the dog, and stays in the annex with the dog. Leaving the dog there when she comes into the main house.
2: She leaves the dog with a sitter, or puts it in kennels.
3: She doesn't come.
Naturally, she'll present option 4 of dog being in the main house, upsetting your existing pets, and how "it's not a problem! Fido is good as gold! Why are you being weird about this?!"
Then you just revert back to "my house, my rules."
It's absolutely not fair to upset your cats for weeks on end, when there's at least 2 very reasonable and easy solutions available.
For what it's worth, I have strong feelings about "being expected to care about other people's dogs." My best friend has a lovely dog, a whippet, soft as anything, real sweetie. I've never had a dog of my own, and didn't grow up with them.
Anyway, about 9 months ago I agreed to do them a massive favour and dog sit their whippet for them in my little flat. I was promised it would be for a "lunch time to lunch time", with one overnight.
They rock up at 9:30am, and basically drop and run. They don't re-appear until 4pm the next day. Texts to chase them up got responses of "we're just stopped at the service station for a break" and "we're just at home now having lunch." When she did finally appear, she came with my 4-year-old god-daughter in tow, and a bunch of flowers, so I couldn't have the "slightly strong words" I'd intented.
Needless to say, I won't be doing them any more dog-related favours, and in their defense, they haven't asked. We've been friends 30 years, more than long enough to read the others signals when they're a bit PO'd.
But the dog was fabulously behaved the whole time, luckily!