Changing an email recipient

If I come back to Jotform to change an email recipient or even add an additional recipient, do I have to copy the code again and re embed the form in my site, or does it change the recipient or add another recipient without me having to touch anything on the site?

You don't need to touch anything on the site. Simply go to your forms edit mode, change the recipient, and save your form.

https://www.jotform.com/help/41-How-to-Find-and-Change-the-Email-Address-Used-for-Notification-Email

You will start automatically receiving the notifications in the new recipient email address.

Let us know if you need more help.