I've tried to reorder the Mod-IE but couldn't find the method. From what I can tell from all the tries, there's no way to reorder them.
Uggh! Tell me this is not true!
Though it is not the end of the world, these annoyances are unnecessary and just causes increased frustrations.
Why would they not duplicate the functionality that exists in Desktop IE? That's from where people will be migrating, so of course they are looking to do/use what they used to do/use in Desktop mode.
I, for one, am transitioning to the Modern UI as much and as soon as I can; when I find an equivalent Modern UI app in the Store that provides the functionality I had in Desktop mode, I get that app. But in the case of IE, for example, it makes it very difficult to transition to that app because of obscurities like this, lack of Favorites management, etc. Consequently, I still use Desktop IE 99.999% of the time. That's very unfortunate, because I really like the browsing experience (swiping left/right for navigation) in the Modern UI version of IE.
When I read this thread, it just made me realize that I'll be sticking with Desktop IE for quite some foreseeable time, unfortunately, until MS can get its act together and make the two functionally identical.