You said you give them Probiotics.

What type? Is it appropriate for children? Most of the formulations are targeted to particular ages, or levels of immunity.

Too many or too large a dose of probiotic without plenty of food volume to go with it will cause diarrhea, or loose stools.

Vomiting? Upon waking? Have you checked their blood glucose? is it possible this or that one could have Type 1 diabetes?

A simple blood glucose meter now costs less than $20, although the test strips are costly, you can buy them for less on Amazon.

Lactic Acidosis or other serious diabetic issues should have shown up in morning blood work, but it clears fairly quickly in an otherwise healthy person, so it might not get caught by the visit to the doctor.

Finally,

as to all that running around outside, you need to be sure they're not running around bare-footed in a treated lawn, yours or anyone's.

Definitely use a Carbon Monoxide detector in their sleeping area,
and the black mold that could be hiding behind dry wall etc. would be the last, best guess.