As a Dog guy those rules just don't seem very logical...lol. My great Aunt had cats and dogs that all grew up together and they still hated each other so it's good yours get along.
Your home looks like what my Daughter says she wants when she grows up. She wants a house full of cats and dogs, plus horses. Don't think she realizes how much work horses are, but dreams are good.
Had the horses early on. Not only was it a lot of work very expensive.