How do I get my stressed-out, antisocial old cat used to my new, very rambunctious kitten?

About 2 months ago my mom got a new, male kitten. She kept him in her room for a few weeks, and for about a week would very briefly expose him to the old cat, a 3 or so year old female who tends to be hostile to anyone new, human or animal (she growls and hisses at the sight, sound, or even smell of a stray cat outside, and reacts similarly to any person she has not known for several months, especially if they're ever loud). The cat would hiss and growl at the kitten, and bat at her paws under the door (our house is small and there's no way to put more than 1 door between them, every room shares a door with the living room). Last month mom released the kitten from her room full-time, despite my warnings that it was too much too fast and would only lead to trouble, and it's been constant stress for the old cat the whole time. The kitten was initially afraid of the cat, who would constantly hiss and growl, and when the kitten would try to go near her to smell her the cat would bat at her. But soon the kitten stopped putting up with it, and would bat back. He began to enter the play-fighting phase and in addition to constantly pretend-attacking my mom, sister, and me, he would ALSO do it to the old cat, chasing her around the house ceaselessly. The cat began to get VERY stressed out, even becoming hoarse from all the growling and angry meowing. Even when the kitten wasn't doing anything at all, she would start to growl and stare whenever she saw the kitten. The kitten started eating the cat's food and water, so mom put them up on the kitchen table (don't worry, we NEVER actually use it for anything other than laying out laundry) so the kitten couldn't reach. This lead to the cat staying almost exclusively on the table and in my sister's room, her favorite place. The kitten started going in there, too, though, but after about a week of the food being moved the cats seemed to get along a tiny bit better. The cat would hiss less, but the same stuff still went on. Then last week I changed the old cat's cat box, and this made the kitten curious. He kept going in it, and I'm not sure if he used it or not but it seems like he did. The cat, always trying to avoid the kitten at all costs, would not go near her litter box and when we woke up the next morning, she had pooped all over the table and on one my shirts and some of my sister's clothes. According to my mom, though I've seen no evidence of this, the cat's fur started falling out, and fearing for the cat's health, she made a post on facebook offering the kitten for adoption to any of her friends who wanted it. I really like the kitten, more than the old cat, because where the old cat is antisocial and rarely wants to cuddle or let us pet her or do anything other than lay on my sister's bed while she's away, the kitten is very affectionate and fun, and is significantly more friendly to everyone, even the old cat, who he still tries to be nice too when he isn't chasing her around. We couldn't make the kitten stop chasing, though, so in an effort to prevent mom from getting rid of him, I dumped a ton of stuff from my drawers in my room to hide my multiple game consoles and their cords (the old cat is a horrible cord-chewer and I'm not taking chances, it ruined my gamecube and ps2 cords), cleaned my room, and moved the kitten's litter box and food/water there. My plan is to keep the kitten in my room at the very least long enough to let the cat calm down, and hopefully for the kitten's play-fighting phase to end. The kitten doesn't mind staying there when I'm there, but when I leave my room he cries, and the old cat will come and hiss at the door. I can't keep the old cat from going near my door, it's in a hallway connected to the living room and it's between there and my sister's room, and I don't know what to do. I desperately want to keep the kitten, I'm home by myself much of the time because I'm still searching for a job so I can move out (and I plan to take the kitten with me), and the kitten is the only real company I have because the old cat never wants to be around anyone more than a few minutes at a time. I want to reintroduce the cats later much more slowly and gradually, but I'm worried mom has ruined any chance of them getting along with her rushed introduction. The usual methods of introducing cats and kittens just don't seem to work, my old cat is just too hostile. But there's no way my mom will consider getting rid of her in favor of the kitten, and I can't keep the poor kitten locked in my room. And I'm worried what will happen to the kitten if we get rid of him. I just don't know what to do, I'm not going to give up the kitten without a fight. Are things already ruined beyond repair? And if not, what do I do?