I was able to put together a sample that uses both the Web Site Project type and the Web application Project type.  As Shaun mentioned in this blog post http://www.dotnetnuke.com/Community/Blogs/tabid/825/EntryID/434/Default.aspx  the core needs to always be available as a Web Site Project to support users that are using the Express edition of Visual Studio.

To use this sample you will need to download WAP here. http://msdn.microsoft.com/asp.net/reference/infrastructure/wap/default.aspx

The approach I took was to create a web application project within the directory of the website project.  To create the sample I took the following steps

1. Create new DotNetNuke website using starter kit
2. Add express database and make sure site works
3. Add widget module using directions from this link http://forums.asp.net/thread/1114393.aspx
4. Remove Widget files from app_code and desktop modules.  I did this so I could create the WAP for the widget module
5. Add WAP for the widget module in the desktop modules folder of WSP I had created in step 1, copy the files back into this directory.
6. Add code directory to widget folder and add files that I took from the APP_code directory
7. In visual studio select show all files and include the files in the project
8. right click each control and convert
9. On the project properties set the build directory to the BIN of the main solution
10. I had to add a few DLL references and add some import statements

One issue I had was that in the ascx you will see errors for the dnn controls.

This could be resolved if these controls were converted to server controls.   I was also able to debug by attaching to the aspnet process.

You can download my sample solution here

http://www.corderman.com/DNN1.zip

Donwloaded, followed instructions.  Two errors related to the code below

The error is 

'Text' is not a member of 'System.Web.UI.UserControl'. C:\Documents and Settings\fnguyen\Desktop\wap\DNN1\WebSite\DesktopModules\Widget\EditWidget.ascx.vb 127 37 Widget

After commented out these two lines, compiled success.  Verified that widget.dll is in the dotnetnuke bin folder.

Coping "controls" folder from dotnetnuke mainfolder inside the desktopmodule\widget does not seem to resolve the error.