Playlists disappearing and playing interrupted in Spotify Premium for Family on iPhone

[Grimslov]

I have had a Premium account for long (without any problems), and now I have changed it to a Premium for Family, to allow my wife and children to get Premium accounts as well, with me as the administrator.
So, yesterday my wife created a Spotify account for herself, and then I added her among my Premium for Family accounts. She got the link and activated it and it worked. So far so good, but then the strange things begin.
She can now access Spotify on her iPhone (iPhone 4), but she can never play more than one song, then it all interrupts. And the playlists she creates (or rather some of mine, which she follows) keep disappearing; she creates/follows a list, then she exits the Spotify app, and the next time she enters Spotify the lists are all gone.
On the computer, on the other hand, her Spotify account works fine - the playlists show up there without disappearing from time to time, and her music can be played there uninterruptedly.
Shortly, you can say that her Premium account on the iPhone behaves like a Free account - very limited, nothing works!
Why is this happening? Her Spotify is indeed a Premium account, it says so on the account's main page, so that's not where the problem lies.
And our son, who also got himself a Spotify account which then was included in the Family by me, has no problem with his Spotify Premium on his iPhone (that one is a 5C though).
Another interesting aspect is that I tried to log into my own Spotify Premium account on my wife's iPhone - and then the same thing happened to me! My lists were not there and it was not possible to play more than one song.
So it seems that it is actually my wife's iPhone that causes the problem, but that is also strange, because my own iPhone is also a 4, and on my phone Spotify is working. Is there some kind of compatibility issue with her iPhone and her new Premium-as-a-family-member account? In that case, how could it be and how can it be solved?
(We have already tried uninstalling her Spotify and then installing it again. It does not help.)