Screen doesn't rotate when Home button used to wake iPad Air 2

I made the very sad mistake of upgrading to iOS 8.4. After several factory resets and nearly 24 hours of chats and calls with Apple (doesn't) Care I'm still stuck with numerous problems. One annoying one is... when using the home button to wake my iPad Air 2 the screen often (to always) will not rotate to the orientation in which I'm holding it. If I use the button on the top of my iPad it always works.

Tried reboots - happens...

Closed all apps - happens

Tried hard reboot - happens

Help!