There's a great teaching concept in networking called the OSI model; I
shant bore you with the details, but one of the things to be learned from
it is that an application like OneNote should neither know nor care about
the underlying details of the network.
If you previously browsed the Internet using a 56k modem, then later
upgraded to broadband, you don't have to completely replace and reinstall
all of your applications, right? IE doesn't know or care about how
you're connected to the Internet, just that a connection exists. OneNote
works the same way.
Unfortunately, while you can do a lot with the OneNote section files in
Explorer, changing the order is not one of them. You've probably noticed
that the section files have the same name as the sections. Viewing these
files in Explorer while sorting by name will naturally alphabetize them,
but this does not carry over into OneNote.
Let's try a few things:
1) Can you try to alphabetize your sections again, but first locate a
hidden file called "OneNote Table Of Contents.onetoc" in your Patients
folder (in Explorer). Write down the file's date and time before
changing the order of the pages, and then after closing OneNote. You
should see the file's timestamp change.
2) Try to temporarily copy the remote "My Notebook" folder to a folder on
the local laptop. Can you then rearrange the sections in OneNote and
have their order retained?
3) You could also permanently keep the OneNote files on your laptop, and
use Window's Offline Files feature to copy them to the network for backup
purposes.