InfoPath, in my experience, is usually bad in that scenario. Sure, it will switch the view, then save and then the email fails to send out the correct view. I don't think you're doing anything wrong.
I would suggest opting for a workaround, though. Instead of using multiple views, use one view with multiple sections. Hide and show these sections as desired; for example, you can have a field in your schema (not displayed in your canvas) called "ShowView" and set the value of that node to 1, 2, 3, 4. Then, you can use conditional formatting to hide/show the sections according to the value of "ShowView".
Hope this helps.