As per your updated question, you can't mix Single Page Model with Multi-Page Model. When you load page2.html first
data-role="pageand ONLY first one is loaded. Anything else is neglected.
index.html (first page loaded) - All tags within are loaded into DOM whether Ajax is enabled or disabled.
page2.html - All tags are neglected except for FIRST data-role="page" and its' content, when Ajax is enabled.
When using Single Page Model and Ajax is enabled, you have to place JS libraries/code for the external page inside jQuery Mobile loads external pages via Ajax, it loads ONLY first and neglects any other tags out side page div.