Difficulty with iCloud verificiation over home wifi
I'm having a very confusing issue with my daughter's iTouch6 and my other daughter's iPhone5s when they are on our home wifi network. Both machines can't send or receive images on iMessage and both have verification errors when logging into iCloud. Other uses of wifi seem to work ok (regular text-only messages, using Safari, etc.). All functionality is fine on my wife's iPhone6 Plus and my iPhone6 using the same wifi network. I've tried resetting network settings. I've tried restoring the iTouch as a fresh machine. I've tried a few other solutions found online to no avail. The problems persist so long as they are on the home network. As soon as I tether them to my iPhone and use cell connection (not wifi) they work fine.
Anyone have any ideas?
iPod touch, iOS 9.3.1