Is it possible to train dogs that had to be separated for fighting, but can be trained to get along?

Not enough information to give you any positive advice.

Age and breed of dogs.

Gender of dogs.

How long they have lived together.

How many dogs you actually own and their ages and breed.

This is an issue that really needs to be discussed and 

shown  to a hands on, good dog behaviourist as it 

appears you have multiple dogs that live as a pack.

Its not something that can be sorted from advice on a dog forum, as it would more or less just be guesses as to the root of the problem which is more than likely

a Hierarchy problem within the pack of dogs, and especially between two younger dogs that are not yet fully mature. 

It is a combination of dog on dog aggression & territorial behavior.  There isn't anything you can do but hire a professional dog trainer specialized in canine aggression.  But it is not guaranteed that the dog won't fight.  You my have to let one or more go in order to keep peace.  If you have no knowledge about canine aggression, there isn't one thing you can do.  Rehoming may not be the thing to do cause you don't want to hand off an aggressive dog to someone who isn't prepared to deal with it.

It is easier to tame an aggressive dog than it is to build courage in a submissive dog.

It may be possible for a trainer to help with the aggression but you cannot have dogs that fight each other.  You have no control over the dogs.  They do not mix well & something needs to be done.

First, you give far too little REAL and HELPFUL information on the situation.  If you want any worthwhile help or suggestions, lease provide:

The number of dogs in you house, the age of the dogs, the gender or genders, whether any are related, or not.  

Just because you asked about spaying, does not mean we can ASSUME everybody is female.  BTW, if all are 'same gender' that makes disagreements FAR MORE LIKELY.  Spaying ought to be done for for HEALTH reasons; but is unlikely to prevent or lessen aggression between females.

Who do you consider to be the bullies (& why)?

When did the fighting start? No, not the date, the breaking point.  (How many dogs did you have living successfully MINUS fighting?)  And at what point - like when adding more juggling items...... did it go wrong?

What types of fighting (or bullying) have you seen & what are the TRIGGERS?

List ALL of the steps you (and/or your spouse) have taken aside from the mentioned ROTATING of who is loose, to stop the fighting.  How much formal obedience (class) training does each dog have, (if any)?  HOW did you teach the "veteran" dog to be nice?  And why did you feel the veteran had to be corrected or "trained" versus another dog?

How open are you to bringing in a professional?  IMO, you need an animal behaviorist, who can observe the dog & people interactions) and make suggestions based on seeing what is going on IN THE HOME, not a just dog trainer.  "WE" have no idea if any of the dogs are resource guarding, and you may not know that EITHER.  (A behaviorist would.)