Oh, though I just realized-- this might be the problem. MWE and MWGE both look to the right directory ((x86)/steam/etc) to launch morrowind, but MWSE seems to be looking for the oldschool location-- so when I use MWSE to try to launch the launcher it can't find Morrowind.
Anyway to forcibly change where MWSE looks for the launcher?
If you Steam installed into the C:\Program Files(x86) folder then you need to reinstall it first, because the C:\Program Files(x86) folder is the culprit here if you're using Vista/Windows7 anyway, so this is what you need to do to if you want to have MWSE checked in MGE and still running MGE with MWSE enabled, MWE at the same time.
1. Uninstall Morrowind
2. Turn off the UAC (User Account Control) in the control panel and reboot your PC when prompted
3. Install Morrowind in any folder
outside of any related C:\Program Files(x86) folder and the C:\Games folder is fine to install Morrowind or any else
4. Install the http://www.fliggerty.com/phpBB3/viewtopic.php?p=65209#p65209 in this order for MGE and reboot when prompted
5. Install http://www.fliggerty.com/phpBB3/viewtopic.php?f=53&t=1008 and http://www.uesp.net/wiki/Tes3Mod:Morrowind_Patch_Project first then MWE