First tip: never alpha roll a dog. No respectable trainer I know ever endorses alpha rolls. Heck, even Leerburg doesn't endorse alpha rolls and heaven knows they are very much into the whole "dominance theory". If you want to really earn the title of a leader, do NILIF (Nothing in life is free): k9deb.com/nilif.htm

For what it's worth, my dogs have gotten into countless scuffles of this type. It's not a dominance issue with the human. It's an issue amongst the dogs, and it's something they really have to manage and which you have to help guide. Like you already noticed, it was caused by a discrepancy over who could have what - in other words, resources. At the time, it was difficult to tell what my dogs were fighting over, but, in hindsight, I can tell you the three biggies: 1) food and toys 2) attention/affection/petting 3) space (i.e. beds).

Closely examine your house. See how many toys you have lying in the house. See how the dogs share their beds, or if they share at all. See how you give treats. See their sleeping areas. Do they respect each others' spaces or does Annie intrude a lot? Does Annie push to the front when you give treats? Does Annie walk ahead of the others/push them out of the way?

So how do you stop it in the meantime?
Clean up the environment and watch what you do. Enforce NILIF. Begin cooperative feeding and petting (feed/pet Pippin and Frodo while Annie sits off to the side. After Pippin/Frodo receive their shares, give Annie food/pets. Then, alternate between the three. This way, Annie learns to wait and to tolerate sharing resources with the other two. If you have any fears that Annie may attack, leash/muzzle her). Practice your recall. Whenever you see Annie about to go into that aggressive "mode" (i.e. you see her staring or stalking Pipping), IMMEDIATELY recall her. If you touch her, you may set her off. The best way to call off a fight is to recall your dog. So practice that recall!!!

You may notice that I don't give any suggestions as to how to deal with the pups when they're actually fighting. That's because, from this point on, you have to work to prevent them from fighting at all. The more the fighting is allowed to continue, the more the behavior is reinforced. So you have to hit it at the cause and prevent them from fighting in the first place.