Skipping all of the hysteria and suppressed hysterics to the point -
Three of the four goat babies are ok, the last one is ... in shock. She is not bleeding, does not have obvious limping or dents, does not seem to be hurting, is walking/standing in a daze. Of course, the more truly hurt the goat is, the less she has to say about it. So besides having looked her over, my best course of action (I guess) is to leave her alone and hope that her mom and brother can bring her out of the shock.
Because a friend was over, I erred on the side of total emotional control. I did not collapse in hysterics, nor did I beat the living shit out of the dogs as I should have to teach them a lesson they would not dare forget.
On the positive side, the dogs will still come when I call.
On the negative side, the dogs have no idea that I will beat them to death if they lay mouth on a goat baby again.