I feel like I'm missing something. I'm surprised that the iPad 2 and 3 behave so differently under iOS 9. It works perfectly on the iPad 3. Obviously the graphics subsystem is very different because of the hi-res screen on the iPad 3 compared with the iPad 2, but you would expect any bugs to be confined to graphics related areas such as drawing, and possibly layout assumptions because of scales factors, font sizes, screen size and so on. Kitz' symptoms seem to indicate a general sick puppy, a kind of malaise, with all sorts of functions not working. Perhaps it's again back to layout and scale factors, but not with graphics, rather with the pointing device coordinates being in totally different value ranges. Sheer speculation here, but based on many years of experience with o/s development on this kind of system and hundreds and hundreds of bugs encountered.
Perhaps Apple were ridiculously slack and simply did no testing to shakedown the behaviour on a non-retina system such as iPad 2. If so, then that's really poor don't-care management, as well as developers who simply can't be bothered to deal with the old res, and who ended up with a mountain of #ifdefs which simply needed to be tightly controlled so as not to turn into a pile of death spaghetti. But all the #elses simply got out of control. That's a scenario I could understand.
It would be interesting to get hold of an iPad 2, completely wipe it and install iOS 9.1 on it clean, then test it, then restore you data set onto it and retest. This way we can see if either something in the config is evil, or else if the in-place, non-cold / non-wipe _installation program_ for the OS is bad, and only a cold / clean install works. For example, on a Wintel PC, I never ever do o/s warm installs of NT, I always do cold install, and then migrate user data back by hand, in case the warm upgrade install programs makes a dog's breakfast out of tweaking the existing, running o/s.