Under View, Print Multiple Views, you need to check all the Views that can be printed. I unchecked 'Use these settings as the default settings for printing the form'.
In code under a button, if you Switch Views to your print view and then call the Me.Print command, then InfoPath will Print the view you switched to and only that view(see code below). The only problem with this is that in that same code, you can't switch back to the view that holds/called the me.print command as you get the error message: "InfoPath cannot execute any view-related object model calls. The view is not ready." A quick search on this error message doesn't yield anything promising.
I'll keep plugging away and see if I can come up with a better way. Otherwise, I may just force the user to hit a 'Back' button on the Print View.
'switches to your Print View
Me.ViewInfos.SwitchView("PrintView")
'Prints out your Print View.
Me.Print()
'Can't do this - you get error message
Me.ViewInfos.SwitchView("SelectExistingRecord")