Sophie Evans' fix got us at least able to access my son's local world's again on our iPad, thank you. For us, this issue is quite clearly related to Xbox live account settings.
Yesterday I set up a new Xbox acct for him and for myself, but I didn't have time then to edit his online privacy and security settings to allow LAN games. I came back just now to do that. He had already opened the game and was playing without issue when I logged in on my Android phone to change the settings.
The page instructions say the changes take affect after logging out and in again, so I had him close it down and open again. It immediately, and for the first time ever, started crashing while trying to log in to Xbox live. He was logged in to Xbox live before I changed the privacy settings and had no issue. The first several times we tried, the game would simply disappear, but eventually we did see a "Global Resources Reset" toaster message pop down briefly before it was gone.
After turning on Airplane mode he is able to load his worlds, but the game is now freezing after a few minutes of playing, and has to be forced closed. I'll be searching this issue from the Xbox live angle and see if it brings any solution.
Just updated my son's iPad 4 and he had the same issues until he logged out of Xbox Live. Now he is playing his local worlds without lag, but he is still seeing the random view shift.
Try logging out of Xbox!