I'm new to these boards, but not new to Navy Nuclear Power. I served for 8 years on submarines as a Nuke MM and got out as an MM1/E-6. I have seen it all.
One thing you've not mentioned is being stationed to stay closer to your wife. Keep in mind that while you are in boot camp, A-School, Power School, and Prototype, you will be stateside. There's no way around that. Since it is not a sea-going billet, chances that your wife will be able to transfer to those duty stations to accompany you are slim. The time you will spend at any one station is short, maybe too short for her to transfer even if she has a job that is supported at those commands (Yeoman, SK, etc).
Once you finish prototype and get orders to your first ship, you still may not be able to be near each other. In order for you both to be at the same duty station, you both need to have jobs that are supported by that duty station. Let's say that you become a nuke MM and your wife is in aviation (mechanic, electronics, etc). That limits where you can be stationed and both of you be at the same duty station. As you get promoted, those limits become more severe.
You could be stationed together, but I doubt it. Unless of course, your wife is a Navy Nuke as well.
I DON'T CARE WHAT A RECRUITER TELLS YOU!!! The needs of the Navy always prevail. If this is a short-term (6 and out) risk they two of you are willing to take for the long term gain, then go for it. If you're looking for a way to end your marriage this will definately help. It can be done, but it's hard and takes commitment.