you could try this:
To exit the application:
Application.Exit();
to kick start another process:
System.Diagnostics.Process.Run("path\filename.ext");
this would apply for both apps, your current app and the updater. Does this help
Have you looked at using ClickOnce to deploy your application It automatically does what you describe.
http://msdn2.microsoft.com/en-us/library/142dbbz4.aspx