Can't say I've done much with InfoPath and Email. Yet in the design of your form, why not remove borders and shading from the control.
Dates are always 'fun'. If it was publishing to a SharePoint library. I'd do the following. Remove your date control and then add a date control. Not a text box and then change it to a date control. When publishing to SP the library sees a single line of text, not a date picker. It might be a similar scenario here.