A SharePoint workflow might be a good way of handling this situation - you will need to at a minimum design the workflow in SharePoint designer though as the out of the box SharePoint workflows won't have this as one of their workflows.
If you want to add a second submit button that pushes the form to any users MyStie you could look at our qRules tool, we have a command that allows you to Dynamically set the submit library for the form XML.
See this users guide on the steps invovled:
http://www.infopathdev.com/files/folders/qrules/entry54050.aspx
Hope that helps
Ted