I have a total of exactly ZERO goat experience, but have been thinking about getting one or two so I've been watching the goat threads here eagerly.
One thing I have noticed about the pics you've posted is that the kids seem 'hunched' up to some degree. Not knowing if this is a normal appearance to goat kids or if this is due to what they were doing/angle of camera at the time the shot was taken, etc, I've not posted about it.
However, a post here regarding White Muscle Disease does mention hunching and drives me to post now. I'm not trying to be critical of anything in any way, just wondering if I'm seeing things.
Lastly, I can't tell you how sorry I am for your loss. I can only imagine the shock and horror you must have felt this morning.