J1234,

There is no way to prevent the Ribbon from minimizing when a RibbonTab is double clicked via a property or method.  If you would like to submit a feature request for this functionality, you can do so here.

Theoretically you can create a class that inherits TabItemUIElement and override the OnDoubleClick event.  In order to use this custom class, you will have to create a creation filter that replaces the RibbonTabItemUIElement with your custom class.  However, this might cause problems with some of the Ribbon's other UI, such as contextual tab groups, since you will be bypassing the default RibbonTabItemUIElement and creating your own.

~Kim~