In the meantime I tried Amazon Kindle for iPad. It didn't look bad at first, but then I tried VoiceOver. It didn't work at first - then it crashed hard. I had to reset the iPad.
Since I bought the iPad for my visually impaired mother, this was not good.
That's a shame, because I would have liked to have bought books for her on Amazon then put them into a shared Kindle account.
Update: This is weird. Ever since the Kindle debacle, if I try to use VoiceOver the screen goes black. Turns out I'd activated the top secret "screen curtain" feature (limited documentation). A 3 finger triple tap turns it on and blanks the screen. I think this only happens if accessibility is turned on. If VoiceOver is off then three finger tap zooms the screen (not so useful actually, just enlarges pixels). For my mother the "Screen Curtain" will be a bug, not a feature!