OK - I know why the code was being called twice.  I had the "AddHandler" code and also defined the sub as the Click Handler (like below):
                AddHandler ibOption.Click, AddressOf btnSaveToDOT_Click
and
        Private Sub btnSaveToDOT_Click(ByVal sender As System.Object, ByVal e As System.Web.UI.ImageClickEventArgs) Handles ibOption.Click

---

Now, as far as "ModuleID"...
In my Click Event Handler for my custom button (btnSaveToDOT_Click above), if I put the code in below:

            cntlCE.Text += "ModuleID: " & ModuleID & "<br>" & vbCrLf

I get a squiggle line under "ModuleID" saying that it's not declared - I then get a compilation error with the same error.

Is the ModuleID being edited stored in PortalProperties or some other object?  I can't seem to find any HTML Editor Provider documentation from DNN, otherwise I would continue looking myself. 

Thanks for the help Adam!  I hope you can help me further with this problem...