My 3 children have all had flu symptoms that included vomiting and diarrhea. With our first kid we spent a lot of time at the docs, but quickly learned that they just sent us home with the same common sense directions of Tylenol, fluids, rest, and the b.r.a.t. (bananas, rice, apple sauce and toast) diet to help combat the diarrhea. For kids number 2 & 3 we were far less nervous and took care of it ourselves. I don't think that made us bad parents.
We've also had our kids go through the sick at night and better during the day routine. If the fevers breaks, the kid perks up and the diarrhea seems to be under control, then it's very tempting to take them out for some fresh air after the kid has been stuck home for days. And sometimes the diarrhea or fever returns, so it's back to bed. It happens.
What you posted does not equal neglect or abuse, but you are really considering a call to cps WITHOUT EVEN TALKING TO THE PARENTS FIRST?!?!
What if nothing is wrong and some nervous social worker pulls the kids from the home for further investigation? It happens all the time. Later, nothing is found and the kids are returned, but they've had to suffer through being yanked from the home and put in foster care. Who wins then? How to you make a 6-year-old ever feel safe again after a cop has snatched them from their own home?
I know it is tempting to play protector of children on the Internet, but hopefully that is as far as you will take this. Keep your medical second guessing and speculations to yourself, unless you have some real evidence that you haven't posted so far.