That install order is really irellevant.  The patchers for FS don't have anything to do with 2142, heck you could install FS without 2142 even installed.  The issue you're having, since it doesn't even have the FS menu, sounds like a shortcut problem or perhaps an install to the wrong directory.  What I've seen to be the best solution to this is:
1) Completely uninstall FS
2) Reboot your PC (Don't skip this!)
3) Install FS 1.2, make sure the path to the 2124 directory is correct.
4) Patch to 1.25 or 1.3
5) Patch to 1.3 if you went to 1.25 first
6) Validate your mods/FirstStrike folder is 1.06 GB (1,145,570,897 bytes)
7) Validate your shortcut points to either your BF2142Launcher.exe or BF2142.exe
8) Validate your shortcut contains +modPath mods/FirstStrike

If you follow all those steps, it should work for certain.

So I followed all of those steps.  The one difference I encountered from the 1.2-1.3 update, from the 1.25-1.3 is this:

Anyone?