I may be wrong here, but so far my experience with the Immigration here leads me to believe that:
Your wife should enter on her Irish passport, otherwise her US Passport will be stamped for a 6 month visitor stay. The Irish passport entitles her to work here. I think anyone with dual nationality should enter the country on that country's passport. Anyone know otherwise?
In your case, I think that once you've received the Irish passport, that it might automatically alters your status. You would no longer need a work permit as you'd hold the Irish passport. Things aren't as complicated here as they are in the states.
I can tell you who would know, you can find Scrumpy over at the forum on
www.americanexpats.co.uk, she is a dual citizen and probably has some good advice.
Best of luck, let us know what you find if you can.