Hi Diana,
I don't think there is any way to silently submit the form by email. Each of the three ways of submitting a form by email call the email client, which the users sees and can react to. I suspect that it is possible a security issue, that the user has ultimate control of the email that is sent.
You could include a small bit of static text next to the submit button (or a tool tip) to inform the user that the form is not submitted until they complete the send operation in their email client.
Good luck,
Niall