Cats are highly territorial animals, and predominantly solitary.
If an adult cat has had the run of the whole house for a long time, it is not going to take kindly to an interloper. So many people believe they can simply mix up as many as they fancy, and wonder why there is friction.
I used to have 2. They came together from the sanctuary, and they told us they were sisters (believable, given markings and apparent age). Totally different in character, they were a complete pain and forever at each other. Continual battle for territory in the house. Would sleep as far away from each other as they could manage. A year ago, one had kidney failure and had to be put down, and peace immediately descended. The remaining puss blossomed, already eccentric personality became outrageous, and we adore her more than any we've ever had. Never met such a character, and much, much happier than when she was at loggerheads with the other. Frankly, I would not attempt a multi-cat household again. It does work for some, but it's not fair on the cats when it doesn't.
I would go very, very carefully with the kitten, and don't push it if it doesn't work.