If you're on a long holiday in Verbier area and small children get sick, just head for the Swiss healthcare system hospital in Sion with pediatric consultation. It's free with the EU health care card and the service is great. You can find it by exiting the highway to Sion Est and following the hospital signs, and the big orange building in the horizon towards east. The drive to Sion from Le Chable took just 40 minutes.
And don't bother with the Verbier or Le Chable doctors which shut doors on your nose if you happen to come just five minutes to lunch time.
I hope we have more sick days behind than ahead of us.