I'm bunny-less and pet-less right now in general so my answers will go back some time to when I did have rabbits, dogs, and cats in the same house.
My dogs and cats growing up were used to bunnies being in the house. And, conversely, the rabbits were used to the other animals. So, all in all, we had a pretty good group of pets that got along well with one another. Or, at least accepted each other, as the case may be! It seemed that no matter the personality of my rabbits, they always seemed to rule the roost over the dogs and cats. Maybe I just had a bunch of scaredy-cats running around (literally!) but my cats never tried anything with the bunnies - they deferred to them. It was always so funny to be in the same room with cats who seemed to be fearful of messing with the buns! When those bunnies came hopping in, it was hilarious to watch the cats run and take cover! The dogs didn't run or hide from the rabbits, but they also didn't pay them much mind. And, I know I saw the bunnies steal their toys from time to time. Again, it seemed the rabbits were the bosses of the house. Despite their pint-size, they seemed to rule with an iron paw!
I'd love to one day have rabbits and other animals together again. I think it definitely added to the experience. But, for now, I'll just wait anxiously to bring my house rabbit home!