I assume by protected form you are talking about a protected form using legacy form fields?
Legacy form fields are not compatible with radio buttons, though you can emulate them with check boxes and macro code; however macros required to make a form work should not be used in e-mailed documents as they tend to fall foul of security arrangements and you have no ability to force users to run them as that would open the window to malicious code.
I would also recommend that you don't copy the form to the body of the e-mail message. For one thing it won't work as you have found and for another, you have no control over the e-mail client that the recipient uses and not all behave similarly.
Furthermore, collating data from e-mail messages is rather more complicated than doing so from Word documents, so you are just making the job more difficult for yourself.
I would recommend that you convert the form to use content controls. To aid that you may find
http://www.gmayor.com/insert_content_control_addin.htm useful, and send the form, without macros as an attachment.
Content controls are much faster to process than form fields (especially with Word 2010 which is up to 6 times faster than later versions). You can have the form protected - the above link explains more - or you can just protect the fields. There is no radio button control, but you can use list boxes to achieve the same end.
http://www.gmayor.com/ExtractDataFromForms.htm will help with the data extraction.
Have you considered making the form as a web page on the company web site and providing a link to it?