Wow, all of this may actually work, but it isn't how you need to install it. Here's what my directory installs look like:
C:\Games\Enemy Engaged - Apache vs Havoc
C:\Games\Enemy Engaged RAH66 Comanche Vs KA-52 Hokum
The trick is that you must install EEAH and then run it completely the first time. THEN install EECH. Then install the allMods patch. Then when you run EECH, it'll detech EEAH just fine.
I altered my installation directories, but GOG's default install directories should serve the same purpose. I imagine the problem you are running into is that you didn't run AH before installing and running CH.

Compatibility With Apache Havoc
If you have Apache Havoc installed then Comanche Hokum will allow you to play the Apache
Havoc campaigns and to fly the Apache and Havoc gunships. Effectively giving Comanche
Hokum 6 combat zones and 4 different gunships to fly.
The installed version of Apache Havoc is not upgraded by Comanche Hokum and cannot
play the new campaigns.
For full compatibility you must upgrade the installed version of Apache Havoc to version
1.1E. The upgrade patches are supplied on the Comanche Hokum CD in the ‘Apache Havoc
Patches v1_1e’ folder. Simply launch the patch.exe within the language folder that matches
your version of Apache Havoc. Then run Apache Havoc once to apply the changes.

hmm not sure what I am doing wrong - I have the two games and have installed them into the same directory as advised above - I still cant seem to access the maps from Apache vs havoc in the comanche game. I CAN access the apache and the hockum though. Am I doing something stupid? They are in the list on the campaign screen but when I try and select them I cant go any further - just the cancel button at the bottom. Any help please? I did try installing the community patch and the maps were selectable there but the graphics mucked up so I cant use it. Arrrrghhhhh