I've worked in the nuke waste processing business for 16 years as a Chemical Process Engineer. Before that I worked in the Pulp and Paper industry and before that I worked at the Boeing Airplane Co. as a Mechanical Systems Engineer.
I would find a place to work, i.e. find an actual job in the nuke business that you want. Then tailor your resume to match the jobs they have. I don't think getting another degree would pay off. It isn't really rocket science in the nuke business, and I don't think there's anyone willing to pay big bucks for a second degree.
There's much paper work that really any engineer could do. Even the design Engineering (which I do in the nuke waste business) is not glamorous, because the trend is to take no risk, to just borrow some old proven design/concepts and hire many engineers to analyze and document that design to ensure it's safety/reliability under all the millions of scenarios that one can imagine. But there's also much Mechanical systems work and instrumentation, electrical, at least in the waste processing plant we're building, that I'm sure you could do. I would try to just get in, e.g. by taking some paperwork type Engineering job that wasn't so popular then, once in, transfer to a more interesting job.
Actual nuke power has been very slow in re-starting as far as I can see. It "should" be getting hot soon, but we may be dead before then.
Here is the plant/project I'm working on. I'm sure we have some open engineering jobs, and there's many others with our suppliers, contractors, and other companies/projects associated with this large nuke waste site and others like it around the country. Working on nuke waste (which is going strong now) could be good way to warm up before the nuke power rush. Then again, it's mostly just another somewhat boring, not particularly well paying, engineering job. It's OK though:
http://www.hanfordvitplant.com/