Trying to stop two cats from bullying another...help!

My partner and I recently moved in to a new apartment, and two of our cats are ganging up on another. We're trying to figure out how to stop this. Here's the story...

I've owned Hyphen and Hugo since they were kittens. They grew up together and are extremely social together. Both are "fixed." Hugo is a large male - alert, bold, aggressively playful and dominant. Hyphen is a tiny female. The runt of the litter, she's slightly timid, attention-seeking, and shy. The two of them are often seen curling up together - Hugo grooming her when she approaches him for affection. They're very playful together, chasing each other around and wrestling.

Simone is my partner's cat. Greedy, docile, and solitary, she craves attention from my partner and I and enjoys being the center of attention. She's not playful with the two other cats, and isn't really interested in other animals.

Before moving in together, my partner and I attempted to introduce and socialize the cats. We lived in the same apartment building on different floors. Both sets of cats had their territory, but we'd often bring them to each other's apartments.

Now that everyone's under the same roof, Hugo and Hyphen have been ganging up on Simone. I sort of expected this from Hugo, because he's very playful and aggressive, and he loves chasing and being chased. I didn't expect Hyphen to corner Simone because Hyphen is normally very timid and passive. There's been hissing and growling, swatting and chasing, and some loud fights. Simone's not displaying any different anti-social behaviors like hiding or avoiding any one, but she's gained some weight since we moved.
We don't want Simone to be victimized or upset - we rally just want my two cats to leave her alone. I'm buying some squirt guns today to squirt Hugo & Hyphen when they're bullying Simone. We have two litterboxes and two sets of food. No one's really staked out "their" territory yet since we've moved in just two weeks ago. Hopefully things will die down once territories are established...
Any ideas or suggestions? Thanks SO much!

Hello. I will try to help...

When they "fight", is there any blood being drawn or scratches or cuts on them? I mean, my cats play-fight all the time. Often they growl and hiss a bit, but nothing major and then a few minutes later, they are sleeping all on the same bed.

One recommendation is to put vanilla extract on their necks and the base of their tails. This will make them all have the same scent and hopefully they will be more accepting of each other.

You can also invest in a Feliway Plugin, they can be purchased from Petsmart or Pet Supplies Plus. They are a bit pricey but man are they affective. They are good for any sort of behavioral problems that may be present. It is also good for other problems too like urinating outside the litterbox. Shelters use Feliway, I use Feliway, half the people on this forum probably use Feliway. It's good stuff.

One more thing, a lot of people on this forum don't agree with squirting cats with water or anything like that. If you do it, just make sure you squirt their behinds or backs and not in the face. Try not to let them see you squirt them either. If you do it enough, they could begin to associate your arm extended with an unpleasent thing that is about to happen. Then you turn into the bad guy to be avoided.

Also, is Simone spayed?

Yes, Simone is spayed.

Well, when they fight, my partner is telling me that Simone is getting some scabs.
We'll try the vanilla extract and look into that plugin thing. Does it have any human discernable odor?

I know that squirting cats with water is "contraversial" - however, we use it for two reasons -
First, a short verbal reprimand scares both the offending cat and the victim cat, and we don't want to do that.
Also, if the squirt bottle is at hand, it's a quick instant solution if we're on one side of the room & the cats are on the other.
We never squirt their faces - just their butts and rear areas. (Seriously, years of Duck Hunt on the Nintendo made me a crack shot w/ the water pistol. It's the only gun I'll ever shoot.) We also try prevent them from seeing us as the source of the squirting.

Thanks for the suggestions!