"When your kids are fighting, do you try to instruct them in the middle of that? I often try to intervene but maybe too often - they don't seem to be learning to problem solve with each-other rather than tattling and trying to get Mom to settle things in their favor. I honestly don't know what would happen if I let my kids continue to fight until it blows over or comes to blows, I usually step in and separate them before I can see how they would solve the problem. I know they are generally out of instructional control when they are fighting, so anything I tell them at that point isn't heard well until tempers are calmed. So, should I step in and try to calm tempers or wait and let them learn to calm themselves and be diplomatic?"
You are right that they are "out of instructional control" when they are fighting.
If the fight is with words, I usually say, "Everyone stop talking...right now (I describe the situation without allowing interruptions)" Then I start with the youngest person and ask for an account of what happened. I work my way to the oldest. I then tell each person what they have earned for not communicating effectively with their family members, and taking the Spirit out of the home. If they don't stop talking when told to , then gently remind them that I just gave them an instruction and what they will choose to earn if they choose not to follow instructions.
If the fight is with fists, I would do the very same as the above, except I would say, "Johnny and Timmy, put your arms down to your sides and sit down..."
If someone could get really hurt and they won't follow instructions, then you will have to restrain them. We can't let brawls happen at home, because it ruins the feeling in the home. If you could get hurt, then don't get involved and call the police. I never want to suggest that, but depending on the age and danger of the child, it could be necessary.
I had to give some of my youth steps for appropriate peer/sibling relations. These helped some of my violent youth.
I don't encourage too many steps though. The best way to keep the family on track is to go back to the family vision and mission and talk about how your family lost sight of what what most important.
Be sure to teach the children things like how to disagree appropriately, etc and do SODAS about it, because that is probably the root of the problem anyway. Have them practice the correct kind of disagreement.
Pray with children who are having a hard time feeling the Spirit or getting along with a particular sibling.
Possibly have positive motivation for successful sibling relations for a few days.
Most importantly, don't ever leave situations like this not discussed, because then they will choose these kinds of power tactics on their syblings more often and they will become increasingly aggressive to maintain control over the other person/people. And, make sure that they earn a negative consequence for their "out of control" behaviors. Cause and Effect!!!
**Don't ever start teaching correct disagreements etc until everyone (including you) is calm. If you have to, give everyone 3 minutes to breath first. If they can't follow instructions to calm down, start the rule of three.