when the younger picks a fight, just put it in the bathroom for an hour of quiet time. Do that every time. The cat is not stupid and will learn finally that mother has no sense of humor when the play gets rough. You cats should be neutered/spayed, but that doesn't always work. There are always cats that are more naturally ambitious for alpha position than others. Impress on your cat through tone of voice and the quiet-time game that YOU are alpha-cat, and you will always step in when things get out of hand. Don't chase with brooms and scream at the cats. that just inspires fight-or-flight adrenalin rushes that only make matters ultmately worse.
Be sure the older cat is not ill, and therefore apparently more vulnerable to a "take-over" bid from the younger cat. If she is hurting somewhere inside, it may make her reluctant to defend herself, thus inviting more harrassment.
Make sure the younger cat doesn't have a pain somewhere. Pain or disorientation can cause a mood or character change in a cat -- at least temporarily.
I have almost 4 years' experience with more than 12 cats at a time (peak time was 21 cats), all living in the house and garden and free to roam if they tend toward the feral. I have seen cats get along wonderfully for the first year or year and a half. Then there seems to be a maturing point where they suddenly decide that it is important who is alpha-cat. This is usually the young males, but it can also be a female. For a while there are spats and occasionally more serious fights, a lot of growling and chasing and sudden lunging... At year 4 now, I have one cat that has never stopped doing this, several cats who have gone to live across the street in an abandoned house and come home to eat about every other day, and the others, who have settled down and have agreed, with a little growling now and then, to tolerate each other. Only a few of the cats remaind bonded to each other in terms of mutual grooming and sleeping together. They have sometimes decided to become best buddies and groom/sleep partners with one of the dogs, and they are ALL bonded in harmony with me.
When any cat changes its moods and agression level quickly, I observe them closely for a while, take them to the vet if I suspect illness or a pain (often this is impacted hairballs or a sore mouth (gingivitus), many ear mites, a cut foot pad (if they don't bleed, they are hard to see, etc.), and if everything is all right, I start my quiet-time routine, lots of extra attention, and my story-telling (it makes them feel singled out and special).
Final try is to give each cat individual attention and petting/lap sleep time as equally as possible. Maybe you've been spending a little more time with one rather than the other...
-----Just jumped up to offer quiet-time to the new cat and one of my 2-year old males. Quiet-time? I repeated to each of them several times. Long, silent, thoughtful stares at me. The new cat actually looked at the bathroom door before he moved off a bit stiffly (not going to RUN away, no-o-o), and the older esablished cat stared me straight in the eyes for a while and then settled back and turned his face away from the new cat -- clear indication of giving up the engagement. This is a typical scenario once the cats understand that I really mean quiet-time. Hitting, by the way, doesn't work and you may end up getting scratched.