I haven't solved it. But I found other symptoms.
When I switched on after leaving it 6 hours it connected ok. Then after a minute it disconnected, asked for the wifi password when I tried connecting again and refused saying the password was wrong. (it wasn't - cutnpaste).
So next I tried connecting my iPad to my iPhone's personal hotspot. My iPhone is on 10.1.1 (14B100), too.
That worked. I changed the password on my iphone's personal hotspot... the iPad connected without me entering the new password!
That freaked me out. Security problem? Dunno. In fact I noticed that the iPad switched on the iPhone's personal hotspot by itself - without knowing the password. That freaked me out even more 😮 I.e. the iPad detected the iPhone's mobile hotspot even though it was switched off and the iPad wasn't connected to wifi. Very worrying (to me)
Giving Apple the benefit of the doubt I logged my iPhone out of iCloud (never realized I was in in the first place). Now the iPad still shows the iPhone hotspot (even when it's off). But trying to connect gives me the message:
Remote Hotspot Failure
Unable to start personal hotspot "xxxx iPhone"
even when the hotspot is on.
All very crazy, and very worrying.