Build the solution, and in Sitefinity drag a Navigation control on your page. Click on the Edit button of the control and set the custom template to ~/MyControls/TwoLevel.ascx (refer to the attached screenshot for more info). This should work once you publish the page.
The Visual Style Builder is still in a beta phase, so your input is highly appreciated to deliver a great final product, in the meantime, please excuse us for the inconvenience some features might be causing.
All that said, I want to point out that exactly thanks to our customers' active participation and constructive feedback we are able to get your viewpoint and try meeting the demands you point out in the forums and feature requests. We appreciate it.