New Puppy, Aggressive Cat

We're four months in and things are still iffy around here. We have 3 cats. None are terrified of the dog, though the oldest cat is the most cautious. The youngest cat will sit near the dog, and will swat at him and he swats back (the dog thinks its a game), and they'll sometimes play chase. The middle cat just hates him, and will hiss at him for existing (I'm like "seriously? the dog is asleep. you are hissing at him for sleeping"). The oldest cat wouldn't come downstairs for a little bit after we brought the (3.8 lbs) puppy home, but now he'll come down, and hang out in the same room - high up where the dog can't get to him when he's awake, and lower down when the dog is sleeping. All the cats swat at the dog, but none of them use their claws ever. Hamilton was afraid of the cats at first, then just decided they were playing with him and doesn't care if the swat or hiss anymore. We're working on it... I generally leave him and the youngest to their own devices since that cat can handle it and isn't distressed by the puppy play, and more closely regulate his interactions with the older two.