In my house, the dogs were there first.

Then the cats started arriving. One by one, until there were twelve.

No nose swats by the cats, but a few loud "No!"s from mom and everyone gets along fine. Of course there are a couple of low gates so the cats can escape if needed.

No cuddling, by cats or dogs. But respect all around.

I don't think it matters who came first as long as they are introduced properly.