Welcome to PT!
In my experience with Taz, I have moved him into a house that had a Cocker Spaniel then the current Aussie we have. He didn't make himself sick over it, but then again these are larger breeds than a yorkiepoo.
And as far as another cat goes. Years ago, I moved in with a boyfriend who had a mama cat and one of her kittens. Taz accepted the kitten pretty quickly. But for the year I lived there he never got along with the mama. They tolerated each other and would sit in the same room, but never got near each other. I think the closest they got was about 2 feet and we were amazed!
So you might be able to bring in a kitten. Just take it slow with the introductions.
Good luck!