I had this problem as well, but figured out a way around it -- but it required some reinstalling of RSII and the sub-mods. I first copied my saved games and put them in a folder on my desktop so I wouldn't lose them. Then, uninstalled and reinstalled RSII. Then, copied the folder that says "launcher" and pasted into the same directory (so you will then have a folder called: "launcher (copy)", or something along those lines. Then, I installed RHE and as you know RHE replaces the original "launcher" folder. Now, at this point, I renamed the folder titled "launcher" to "RHE_launcher", and the folder titled "launcher (copy)" to launcher. I then repeated the step of copying the "launcher" folder. Then, I installed Demise. Renamed the launcher folder (this time with a launcher that opens demise) to "DOTR_launcher", and then once again renamed the "launcher (copy)" folder to "launcher".
So at this point, you'll have three different launcher folders. (1) launcher, (2) RHE_launcher, (3) DOTR_launcher. What I did was copy the launcher shortcut from each of those respective folders (what you'd normally use to start RSII) and renamed the shortcut accordingly. So instead of having one shortcut where you choose all of your various campaigns and sub-mods, you'll instead have 1 shortcut for the normal RSII campaign, one for RHE, and one for DOTR. Hopefully that all made sense. There may be an easier way to solve the problem, but the above worked for me.