Thank you for the reply.
It is not surprising that things may be a little "off" for awhile when you introduce a new cat to the household. The hissing and swatting at your wife is quite normal as well and is known as displaces aggression. Mittens is anxious due to The situation with Ollie bothering her and takes it out on whoever is nearby.
I am not sure how you have been separating him at this time, but when bringing in a new cat, it is best to give him his "own room" for a short while. There are mutiple reasons for this, including making sure he is not incubating any of the contagious cat viruses, like feline leukemia and/or feline aids. If he was not exposed to other cats for awhile previous to coming into your house, he may have already been screened for those however and that would be less of a concern. From a behavior standpoint, it can be a little less threatening to Mittens if his living space is somewhat restricted to start versus being allowed to have full run of the house right from the start. Cats do not really have a hierarchy in the household, like dogs do, but they are somewhat territorial and may be upset if all of a sudden someone takes over their favorite spot or favorite litterbox.
Even when confining him, she will know he is there and she will be able to get used to his sounds and smells through the door, before he is allowed to mingle full force. Even when you start letting them mingle, I would do it slowly and only when you are there to observe at first. If they are left all out on their own, there may be altercations that occur that you are not even aware of. Depending on what the set up of your house is like and where Mittens likes to hang out, maybe you could alternately confine her in specific areas of the house and let him roam around some also. Eventually, the goal is to allow everyone to be out at all times, but it is often best to build up to that gradually.
Most cats do not like to live with one another right off the bat so we have to strive to provide an environment where all cats are able to find a place where they feel "safe". That begins by creating an environment of "plenty." There should be plenty of litter boxes, food bowls, climbing towers, toys and resting areas in multiple locations. All the litter boxes and food bowls cannot be clumped all in one place because that forces the cats together, something they don't want to do.
If that is not possible due to the layout of your home, another option is to create a time sharing plan. One cat is out in the house for a bit, then put into a room and other is then allowed out. In some cases we just use a screen door on a bedroom to keep the cat separate, they can see each other but not interact, this can be very helpful. When they are separated, we can then proceed to limited introductions, where the cats are rewarded for being calm around each other.
To keep Ollie from chasing or bothering Mittens, I would get him a cat harness and a somewhat long lead. When they are not separated, I would attach him via the lead to a table leg or something. The purpose is to allow Mittens some freedom to move about the room, but not allow Ollie to run after her. This is to be a temporary measure to allow the novelty of chasing to wear off for him and to allow Mittens to build up some confidence for moving about in the same room as him. We actually used this with my two cats and it worked great. It was funny, but the untethered cat learned the boundaries very quickly and knew just how far the tethered cat could reach so she stayed outside of that circle when she walked, but she would at least walk in the room with a little more confidence. The tethered cat took a few tries to learn that no matter how many times he tried, he could not reach her. There were a lot of "stare downs" but eventually the newness of the new cat wore off and he didn't seem to care when she walked by him. We only had to use the system for a few weeks but it worked like a charm. Another option would be to allow both of them in the room or area together, but maybe use a screen barrier to separate them. Feed their meals that way, but at a distance from each other, gradually reducing the distance. Don't allow a stare down between cats and keep the cats busy by distracting with playing. Then put one cat away. Always end the encounter on a happy note. An indoor invisible fence or other type of perimeter control would serve the same purpose to create a "off limits" area for one cat.
One other thing I would suggest is a product called Feliway®. Feliway is a synthetic pheromone that mimics the natural chemicals that a cat secretes. It creates a comforting, reassuring feeling that has a calming effect. It is calming to cats in stressful situations such as transport, hospitalization, veterinarian visits, boarding, new environments, pets or people. Feliway® is a product that can be sprayed or used as a room diffuser. It can be purchased through veterinarians and pet stores. In your case, a few room diffusers may help low the tension. LINK HERE
I am also including a link to a website about environmental enrichment for the cats. The Ohio State University has composed this to help cat owners structure the environment to provide adequate physical and mental stimulation. There are numerous medical conditions in cats that are precipitated by stress and multicat households are often those with more stress, even if not perceived by the humans in the house. Hopefully there are some ideas there that you can incorporate to help keep the stress levels under control
OSU Indoor Pet Initiative
I hope this is helpful. Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please reply so I can clarify for you.