I think trying the baby gates, as in three small ones stacked so that they cannot get to each other, is a great idea. I totally agree with Tabbcatt, and think it would be best to keep them apart until new kitty is spayed, and hopefully you can get that done ASAP. I think that could be part of her aggressive behavior.
I have one cat that I have to keep separated from my other three cats. They get equal times with the run of the house and then they are up in their bedrooms when it's not their turn. It is exhausting. Having to make sure doors get closed right away so they don't get out at each other. But my oldest cat was 5 before the next stray came along, and she was never socialized around another cat, and I did EVERYTHING wrong when it came to introductions. I really do think that Beep (mean cat) was never going to be a cat who could be around another cat, no matter what I tried, but I think I made it worse. I did the room swapping, time apart, letting them check each other out under the door. When I finally let Beep out with Taffy (my only other cat at the time) it went really bad. Beep flat out attacks him, jumps on his back, teeth in his neck, chases him under a dresser or couch, and won't let him out. She is relentless, she will not give up, she keeps going after him, non stop. Poor Taffy ends up pooping on himself out of fear. We tried everything to make it work, even tried the "let them work it out", but I think what I did to make it worse was I freaked out every time Beep attacked Taffy. I would scream, yell at Beep, pick her up and put her in her room. I now know that the worst thing you can do is take sides, and over react. No matter what happens, you have to be neutral. Even if you are freaking out inside, don't let the cats see it. They totally feed off of your energy.
Eventually we called it quits and realized that the two cats would never be able to be together, and so we have the crazy rotation cycle, where one cat is out while the other is up. It works, but it is exhausting, but I've been doing it for over 6 years now.
Two years ago, my 3rd stray wandered into my life, and while we were looking for a mommy for him, we fell madly in love with out solid black boy that my daughter named Stephano. Luckily, after a little hissing and swatting from Taffy, Stephano and Taffy eventually bonded and they love each other. So we decided to keep him, since he had bonded so tightly with Taffy, and Taffy now had a companion. I said NO MORE CATS!!!!
Well, then 11 months ago, a sweet little tabby girl wandered into my yard and it was freezing outside, so I let her inside. This was after two weeks of seeing her running around my neighborhood. She clearly had belonged to someone, she was fixed, chubby and a total cuddle bug who curls up in your lap every chance she gets. I figured someone must have moved and left her, or she got out. I put up signs, ran ads on craigslist, and every lost pet site I could find, and no one came looking for her
Off to the vet I went with her, no diseases, healthy, guessed to be at least 3, maybe older. When we went to introduce her to the other two, there was some hissing from Stephano and Taffy, and this little girl we now call Pippi, she was very defensive against the boys, did not want to play or cuddle with them, but she is tiny, like half their size and she learned how to get along with the two boys. She still doesn't love them, she hisses at them and does not want them next to her, but she tolerates them. Stephano has been a little bit of a problem lately. He will pin her down and she screams like she's being murdered. He doesn't do anything to her, just holds her down. I have learned not to freak out over it. I don't lose it and I don't take sides. What I do though is distract them with play. If you don't have the cat toy "da bird", you need to get one. Most cats go insane for this toy. If you have some scheduled playtime with the cats, at least twice a day, you cannot imagine how much of a help it can be. They run out that energy that they are now taking out on each other. Playtime has been the best thing that I have done to keep them all happy together. When Stephano goes after her, I get the toy and he goes insane over it. He LOVES it! When you wave it around in the air, it mimics a bird flying, makes a little whirring sound, I just can't tell you how great this thing is. We go through one every few months. You can buy the replacement feathers for them. After the cats have had a play session with "da bird", everyone is exhausted. No one wants to chase anyone. They usually go sleep for hours afterwards. Another thing that I do is that I give Pippi breaks from Stephano. She loves to spend time in our den looking out the window, she is quite comfortable in there. So I let her spend time in there away from him, not every day, but days when Stephano has been a little bit of a butt, lol, and I can tell he's going to be a problem. When you eventually do let them out together, I would make sure to put the new kitty in her room when you can't be there. This gives them a break from each other and you know they won't fight.
I would also get a cat tree if you don't already have one. Having lots of places to climb up for cats is very important. It also is a great thing for the young kitty to climb up and down for exercise. I have several and my cats love them, they spend most of their time on their tree. Get "da bird", you can find them at Pet Supermarket, Petco, PetSmart, they are about $8. A laser pointer is also a really good thing to get them running around too, although I have found that my cats get bored with that one pretty quickly, but for a younger cat, I think she will love it.
It takes time, and a lot of patience. If they get the point where they just hiss, smack, maybe roll around a time or two and then go to their own spots and tolerate each other, that's OK, and honestly, to be expected. You don't really want to take any action UNLESS it is really bad, there is blood, and it's really just non stop attacking. If it's just minor little hissy fits, it's best to just distract with play, and food or treats, another thing that you can use to distract, and let them work it out. And don't take sides, and don't freak out (like I did). If it's bad, DON'T attempt to break up a cat fight ever, you will end up really hurt. Wait until they are apart and get them separated.
I think new kitty will be much better after she is spayed and doesn't have all those raging hormones making her crazy. You could have a play session with her (after she is healed up of course) with "da bird", get her good and worn out, so that she is has played quite a bit, before you let them out together again.
Sorry i rambled so much. I hope it all works out. Just be patient. It is not uncommon at all for cats to be little jerks when first introduced to another cat. I do think that some of the people on here who have had the most success with cat intros are the ones who just ignore the hissy fits and not make a big deal out of them and let them get used to each other. Sometimes that approach does not work, like in the case with my cat Beep, but most of the times it can work. Best of luck to you.