Why not use UIResponder to jump to the next text field? https://developer.apple.com/library/ios/documentation/uikit/reference/UIResponder_Class/Reference/Reference.html
As to simulate key press, his might help http://blog.lazerwalker.com/blog/2013/10/17/more-fun-with-simulated-ios-events-keypresses/ But he uses private apis, and it only works before iOS7.