Clearly there is some confusion about how exactly side battles affect the main battle. A discussion has been begun on the playtester side and we will try to resolve as quickly as possible.
Thanks. I apologize for stirring up a hornet's nest. I also apologize if my explanations weren't completely clear, as I was still incredulous to myself that I missed it all these years.
I'm afraid I don't follow. Please explain, and use small words so that I am sure to understand. 
I'll try. As I mention above my explanation is based on a past ruling (and I don't know if it's current) that "Fight Each Other" is an instant ability. Many rulings in the past have been based on this. Like any instant ability, it must complete before any other ability can activate. If for example a "capture" ability is activated, we know we cannot play a dominant to impact the available targets. The dominant's ability must wait until the capture completes. Ergo, the same must be true for a "Fight Each Other" ability. A dominants ability cannot activate until the "Fight Each Other" ability completes. In the past this has always been once the side battle completes. So it follows then that a dominant's ability cannot activate during the entire side battle.
That's the easy part to explain using current rules and using the dominant as an example. So what does that mean? What happens with other ability types? What abilities can be activated during a side battle?
A "Fight Each Other" causes another battle to take place. It has been ruled to be a separate battle but NOT a separate battle phase. So we use the rules for a battle to determine what abilities can activate during the side battle keeping in mind it's the same Battle Phase. The first step is the targeting and activating of characters. Why do their abilities get to activate and not wait until the "Fight Each Other" instant ability completes? I think we use the precedent for "Play Next" abilities to answer that. So cards that are normally played during a battle, characters and enhancements, will activate one after the other based on rules of initiative. However, a "Fight Each Other" ability does not allow for the playing or activating of other abilities so we fall back on game rule. At that point, all other abilities must wait until any pending instant ability completes during the Battle Phase. That would include dominants, triggered and optional abilities that were put in play prior to the side battle. That's why a previously placed enhancement will not activate in the side battle if on a character in a side battle.
In any case, Gabe was right that I never went through the rules in the first place. As I said, I was still in a little bit of shock. But now I've layed it out with rules. I don't see any problems with this other than it's something new to get used to. I doubt it will break anything especially since side battles will limit some types of abilities from activating. It may even add a bit of strategy.
