I've been trying to find a way around the same issue as raised in this thread to no avail.
No worries, I fixed it through trial and error.
Just in case someone else out there was having the same basic error and weren't sure what should be added to make the form submit with the enter key, here's what I added to the form...
<input type="text" style="visibility: hidden; position: absolute" />
This is probably common knowledge but if someone out there has only a basic understanding like I do then hopefully this will help them.