Looks like "mama bear" was right in the thick of things, too. She got the kiddos sequestered away, then jumped into the fray with a big stick; probably why they gave her shots, to be on the safe side. A big "atta girl" to her!
I'm impressed by this family and the way they handled this. They not only get outdoors regularly (not the all-too-common couch-potato fatties), but used common sense in taking two adults along with kids in an isolated area. Looks like dad had no choice to handle it the only way he did. But say, he had slipped and hit his head and was knocked unconscious and mom wasn't around, the poor kids would have been left alone at the mercy of this rabid beast.
Also, our Eastern coyotes have been shown to possess both wolf and domestic dog DNA (dad did say it looked like a German Shepard.) Not only larger, but probably also less fearful of humans than their western counterparts.