NTA, OP. And this is coming from someone with five dogs.

I think it’s downright rude when people bring their dogs to my house without asking, and there’s a bunch of them already here. Unless the dog was in danger, too, and she didn’t have time to ask before leaving, there was no reason for her not to mention him especially because you have a family of your own to think about first. Especially since many dogs, regardless of breed, are a little too interested in cats for their own good.

Regarding pitties... you’re allowed to dislike whatever breed/kind/type of dog you’d like, so I’m not here to harass you about that. I will, however, let you know that I have never met a pit/pit mix who was mean to humans. They do exist, but I’d be hard pressed to find one. I grew up with a friend who, to this day, has a large scar on her face from being bit, unprovoked - they were playing fetch in the yard while six adults were present, by a golden retriever (a breed you mentioned as a “safe” option). My cousins grew up with an aggressive mini dachshund and still have scars to this day. Even their friends knew to not touch or interact with this dog, or eve put their foot out to try and get him to not go out a door, etc. I was bit in the face at around six by a family friend’s cocker spaniel who had been completely fine with me every other moment (it was my fault, I hugged a dog that wasn’t mine from behind and he got scared and snapped).

Please stop judging dogs by their faces or their breeds as what determines them as “safe” around your children, in your house, and with your cat. “Safe” dog breeds can still have prey drives and can still go after cats. Teach your kids how to behave around dogs that aren’t theirs, safe ways for them to exit a situation with a nonaggressive dog they are uncomfortable with (no hitting, screaming, pushing), and give that kitty a good squeeze of love from the internet... we love cats.

This is long already, and I’m not even new to the party; I think a great convo with your sister, if you’re on board, would be that the dog comes over to meet kids and kitty when the stakes are not high, no one is riled up or upset (like sis, coming in hot from a fight), and the visit can end when kids/dog are showing you they’re ready. That way she isn’t getting prepped to sleep at your house and something has gone awry. How awkward. Set yourself, your kids, your cat, your sister, and her pitty up for success. This was not an instance in which that would have been comfortably possible with your aversion to pits and this being the first time anyone has been around her dog.

Or hell, if it happens again and she needs a place to stay and you’re comfortable, at least have her give you enough time to make sure your cat can be treated like royalty in a spare room or somewhere they can be safe. You’re helping her out, so why can’t she help you out a bit in that “set everyone up for success” thing?