IDML stories hierarchy

Which CAT tool are you using? 

I have a pile of JS solutions for problems like this, but they're all made for reordering XLIFF IDs, not for reordering story names. So they'd be hard to adapt, but it's doable. I imagine it would be possible to remove all of the stories and re-add them in the TDLR order you specify. That would get your CAT tool to read them in your preferred order, I suspect. Similar tricks might be pulled on the designmap.xml file itself. I've not tried either one, just throwing out some guesses. 

But it's such a bizarre circumstance that before writing even a single line of JS, I would want to know which tool you were using. Because this is not a normal outcome from dropping one's IDML into a CAT tool, and if it's not some in-house developed tool, I would like to be able to either a) figure out how to configure it to consume IDML properly for you, or b) avoid it like the plague. I also am very curious about this little fragment: 

My understanding is that the order of the content is based on the order of appearance of the stories listed in the designmap.xml file.

There are a few places one might look at designmap.xml and suspect that you'd found the "order of stories" such as <idPkg:Story src=or <Document StoryList= but I don't think that either one would work for a CAT tool to collect stories properly. It's Deeper Than It Looks.

I believe that's the purpose of the Articles pane. Each article should be there, or be dragged there to create the list, and then the order can be assigned or sorted.

Not a feature I've used much; others may have better guidance. But look there to see if it's a solution for your issue.