You may need to visit the Acrobat forum and get some help with this.
Aaah I see...
So here's a naive question: why not setting up your document with facing pages?
Wouldn't that solve your problem?
Additional question: do your buttons have to be hidden when navigating back to a page where questions have been answered already? Because obviously that wouldn't be the case: same behavior is to be expected. Besides, facing up pages wouldn't solve that issue.
(question: do you use Acrobat Pro ? what version ?)