The .H files are stored locally on each machine. I keep scratching my head on this one and I think the path may be stored in binary format as well as in the reserved8 field.
Here's what happens: I set my .H file for a class and compile. Another developer checks out the class to do some work and the reference is broken. The class compiles with errors and when the other developer goes in to set the path, it shows the full path on my machine. We both have the same relative path to the file on our respective local drives.

I have seen this happen with class locations (CLASSLOC field) on occassion.
I thought it was due to the developer having a path set to a shared network drive and not to the relative local path, so the class was finding it's parent class library on the network and not locally. May not have been, though.
Have you hacked the VCX to see what it's actually storing?

USE mylib.vcx
LOCATE FOR !EMPTY(reserved8)
MODIFY MEMO objname
MODIFY MEMO reserved8

I wonder if the RESERVED8 field is storing a longer relative path than it needs to.
In your examples, you had D:\APPS2000 and C:\VFPAPPS.
Assuming you have PROJECT1\INCLUDE and PROJECT1\LIBS in both of these directories, is should be storing "..\include\myinclude.h" - I wonder if it's going the extra step and storing "..\..\..\apps2000\project1\include\myinclude.h"

The "include file" dialog for the class designer won't let us specify a relative path. You can save one, but if you go back to look at it, the full path is there. That's the full path the other develper sees when they open it.

Even if it is storing the relative path like it should be, this dialog will resolve the relative path to show the absolute path, I guess to make it easier to tell exactly where the file is.

If you would like to have common access to the same include files, you could put the .H file(s) in a common network drive and in the "Include file" dialog enter the UNC path to the file. This will not be resolved to a mapped absolute path.
I haven't tested actually using this, so I don't know what kind of contention or speed issues this may cause.