Look, I sympathize strongly with the desire to jump in and do something. I'm not going to say that I would not have intervened, as I have a history of doing stupid **** in the name of protecting others... but pausing to make a realistic appraisal of your risks in intervention isn't cowardice, it is prudence.
But, do recognize that from a purely pragmatic viewpoint, jumping in here is taking a big risk. You're going to end up being scrutinized by law enforcement at a minimum; you may be charged; you might even have to stand trial, depending. At best that can cost you more money than you can afford to pay; losing your house and everything you own and having your salary taken-from for twenty years is possible if you lose in civil suit; at worst you could do time in prison away from your own family. It happens.
You have to be aware that if you involve yourself other people might jump in, and the situation could escalate and become an armed battle.
Immediately pulling a gun on a 15yo girl engaged in an unarmed brawl with another 15yo girl is a fairly extreme reaction. Granted, from a purely tactical standpoint taking control through the threat of overwhelming firepower has its points, but legally you're putting yourself in a very precarious position. Playing the hero seems very noble until you're doing 15 years in the State pen in the company of people you'd rather not spend 15 minutes with.
A more moderate approach would be to move close to the fight and yell at the kicker, 'HEY, that's enough! Whatcha trying to do, kill her? Cut it out! The cops are on the way already!'
That might be enough to cause the perps to unazz the AO, as they probably prefer not to encounter the police.
Or it might not... maybe some of the bystanders will threaten you and warn you to stay out of it. This may give you a chance to evaluate the situation and see what kind of opposition you're looking at before you take it any further.
The next step might be physically interposing myself between the girl doing the kicking and the girl that's down. I ain't scared of getting hit by some 15yo girl, I'd be glad to take some of the blows to keep her from kicking the other girl any more... but I have to be aware that the attacking girl just might pull a knife or gun if I do this, and I have to be prepared to deal with that and to accept that the end consequences of my intervention may be very serious. This could include losing my life, or all that I own, or my freedom. I also have to consider the effect on my family/dependents if I am killed, sued into poverty, or imprisoned for a long term.
If you still think it is worth it, in a situation that isn't necessarily life-or-death, then by all means go for it. Just make sure you're fully aware of what you're getting into, and what the final cost might be.
The difference between someone who is a professional in use-of-force situations (ie violent crime), and an amateur, could be summed up as the ability to make a rational assessment of a situation, rather than an emotional one. If you make a rational assessment and believe it is worth the risk, more power to you. I'm not sure what I would have done if I'd been there at the time; it would depend on my on-the-spot assessment of the situation.
In closing... When the machine gun opens fire from a covered position, Private Hothead charges it in the open and gets heroically blasted to pieces... Sergeant Old-Pro takes cover and calls in an airstrike while smoking a cigar. :mrgreen: