Hawkeye,
I'm not sure about the order of the favorites in IE11 when they are "synced" and come over to a 2nd PC. I have always done this manually via a flash drive or via OneDrive or something. I think helpifican is onto something when you use your Microsoft Account on both PCs, I believe I saw my Favorites come over in alphabetical order on at least 1 of my other W10 machines (I have 5 total) through the LAN. I'll check further, and get back with you. Other than the Microsoft Account syncing of folders (Favorites being one of them), I'm not aware of any way to change that order except going into Favorites via clicking on the Gold Star-->Add Favorites-->Organize Favorites, and then use the
NEW FOLDER, MOVE, RENAME, & DELETE buttons to change your folder arrangement manually.
Lobo might be on to something about importing into an HTML editor and using HTML tools to reorder your folders the way you want. Then delete your favorites on both computers using Windows File Explorer. Import your changed Favorites folder back into the Master PC with you logged into that PC with your MS Account, and then log back into your 2nd PC also with your MS Account, and let them Sync up. This might take awhile, such as several hours if your have a lot of stuff on your OneDrive (I have 0.36TB on a 1TB space), and if you also have Dropbox or any other Cloud accounts to sync. I haven't really tested this per se, but I think that one of these 2 methods might work for you.
Let us know if you find a better solution!!
Best of luck,
<<<BIGBEARJEDI>>>