From what I read, WDW called the police, so I don't think that should determine who did or didn't throw the first punch. But we don't know what started the issue (though my $ is on the early ADR/RD issue a la 7DMT), so what ground do you think the mom and daughter are standing? And the mom is the one who started using the umbrella from China as a weapon.
I watched the video again and as others have said, it's really hard to tell who threw the first punch, especially since the heads of other guests keep blocking the view. But, it looked like the one girl came back towards the mom and daughter and they were all yelling for a minute, then mom started swinging her umbrella and that's when you see girl #1 pulling hair and taking a swing at mom. It was a bit confuzzled, but I didn't see girl#1 touch the daughter at all. Oh, and the daughter ran over her little sister and brother and knocked them down during the brawl.