(Here is what I posted in a similar thread on this forum) I'd like to add that keeping them separated is best, even when you KNOW they get along well. I don't allow my cats to provoke the dogs at all. They get a gentle swat on the nose or a spray with water when I catch them doing it, and the dogs get a swat on the muzzle if they chase or taunt the cats. I also redirect with treats. It gets their attention very quickly when I get in the middle of them with treats and say "treats!!" pretty loud. They know the word. I did it when they weren't chasing down the cat, but when they are calmly checking them out. That way I was only having to talk to them. Now I have to raise my voice if they are distracted with the cats but "Treat!!" works well now.
I have 2 fixed male cats, brothers, that are ~2 years old. We rescued them from a family who had too many pets. They were less than 14 weeks old when we got them. They had several dogs, but the dogs were "outdoor only" dogs. They went almost a year without ever seeing or being around a dog again. When my boyfriend and I had to move when we hit some rough times, we stayed with his parents for a few months. They had a Scottish Terrier, only 2-3 times the size of our cats, and another cat also lived in the house. Their cat was indoor/outdoor, and they had a few scuffles. Out cats HATED that dog. She had several health problems, including major food allergies and hot spots everywhere. They would pick on her every chance they got, peeing in her bed, stealing her bed, etc (yes, the cats won every time). Lady, the dog, would not defend herself. She wouldn't bark, nibble, growl, bite or anything else. If she did, it was a quiet growl and we almost never heard it. Less than a year later we own our own house with 1/2 acre in Southern California. We made the conscious decision to purchase not 1 but 2 puppies from a local breeder. They'd never seen a cat before. We didn't know if our cats would be ok with it or not. They, generally, get along just fine. Sure, the cat will run and the dogs will give chase sometimes. If they do, I tell them "leave it" very firmly. Most of the time they do, but if they don't I use their names and that gets their attention. However, we have two rooms that have "pocket" doors, the kind that slides into the wall so they are almost impossible to open by humans much less by dogs. We leave one of those doors (leads to the master bathroom which contains the litter box) open the width of my fist (which is pretty small), and the cats can just squeeze through without hurting them. I treat the dogs every time they give chase but leave it when told, so they learn that NOT chasing the cats gets them a treat, but chasing the cat means a "time out" where they sit on their bed for 10 minutes without crying. Both of my puppies are male, unfixed and ~13 weeks old now. I'm losing track, lol. I feed the cats on a large high table where the dogs can't reach the cats food bowls. They seem to have learned very quickly that it's not their food because I'll gently flick them on the muzzle. They mouth the cats, snuggle the cats, lick the cats. Some times the cats tolerate it, sometimes the cats lick, nuzzle or mouth/bite back, and sometimes they could care less. I just make sure that the dogs have a cat free zone (outside, with us) and the cats have a dog free zone (the bathroom in the master, and the master closet too). The cats keep the dogs in line when they don't like something, and the dogs have learned really quickly. I only interfere in their "play" when it looks like one or the other may start to get too rough. I punish neither if they are being "gentle" in their play, though sometimes it's hard to tell if the cats are playing or genuinely irked off. The other thing I do, every time I see my dogs with the cats is "gentle gentle gentle". I tell them this when they take treats, and they will take the treat with lips only or barely get their teeth on it using almost no pressure. They learned to use the same idea with the cats too. Most of the time. I've even caught a dog and cat napping together once. We've had the dogs for less than a month. Give it time, set clear boundaries, give them both their OWN personal space away from the other. No cats allowed to torment dogs while in their crates, etc. When Blitz and/or Degen are being extra calm, I'll grab a cat and sit him about 3 feet away from the dogs, then hold the dogs in my lap so the cats can sniff and check them out with a "safety net". You can also use a leash. Just don't allow them to hide all the time from each other, they need to spend time together too, even if it's just walking around. I gave the cats one of the outgrown dog collars to play with (for the scent) and the dogs a blanket the cats use to sleep on (for the scent) as well, and that seemed to help a lot. I've done the same thing with family that the dogs were afraid or leery of, giving them a ratty old sock that they wore for an hour or two, or a rag of a tshirt, etc. I can't say that your dogs and cats will be good together, but don't panic yet. There seems to be no reason. I think in due time they will at the least learn to ignore each other. Hyperactivity in the pup around the cat isn't surprising, mine were both that way with our cats at first too.