My family has adopted a Golden and a yellow Lab (they thought he was a Golden-Lab mix, but he sure doesn’t look it) from a Golden rescue organization. Rusty, a very red Golden, has some ongoing storm phobia problems but with the help of family and occasional medication, he’s doing fine. He’s a total goofball and very sweet. Isaac, the Lab, is one of the best all-around dogs I’ve ever met. He’s very very smart, learns like THAT, and loves people. Except for the Fed Ex guy. For some reason, they BOTH chase the Fed Ex guy. I think they just want to play, but it scared him the first time.
Rescue dogs can be great, and reputable organizations will know as much as is possible to know about the dogs they put up for adoption. I LOVE those dogs, and I don’t get to live with them.
The cat, on the other hand, does not like the dogs one bit, and is usually outside (don’t get on my case about that) or in the master bedroom, which has a window where she can come in and out whenever she wants. A well-established cat is probably not going to like any dog coming in, especially one that comes running over saying, “Ooh, I want to PLAY! LET’S PLAY!”