Just to toss in a perspective. If your BF/hubby/whatever decided to get out and go to work for a company that is a government (more specifically defense) contractor, they will know what the DD214 is and means. IF said job requires a security clearance, they WILL find out what the circumstances are, do not lie. PERIOD.
There are many options out there. If y'all are fed up with nuclear, you can find non-nuclear jobs. My personal advice, based on the inputs from the OP, use the GI bill. Go to school get the college degree, most preferably an Engineering degree. That will open many doors, both in the Nuclear industry, and non-nuclear industry. The future prospects for degreed engineers are quite good. There is a global shortage of Engineers. Even more so in the US and Europe. Especially for Engineers from good quality schools.
As for cross rating, that's between you two. If you like the Navy, go for it. Just bear in mind that life as a non-Nuke is vastly different than as a Nuke. Two different worlds.