From the information you've provided, it's going to be an uphill battle for you to secure U.S. citizenship because naturalization applicants must be residents of the U.S. at the time of application. First we'll backtrack a bit and look at some of the other requirements for obtaining citizenship. Applicants must have maintained permanent residency in good standing for the five-year period prior to filing the paperwork. (For those who obtained permanent residency based on marriage to a U.S. citizen, this period is three years.) Good standing means being a person of "good moral character," - i.e., staying out of trouble with the law, complying with U.S. tax laws, etc. - maintaining a primary residence in the U.S., and meeting the physical presence requirement which says that naturalization applicants must have spent at least half of the five year period - 2 1/2 years - physically within U.S. borders. Looking at this requirement more, absences of one year or more will break the physical presence requirement, and the permanent resident would have to start counting a new five-year period if naturalization was the eventual goal. An absence of more than six months but less than a year could be considered a breach of physical presence unless proven otherwise, while an absence(s) of less than six months is permissible. You say that you've held a green card since October of 2004 and moved back to Ireland in July of 2007, which would indeed give you 2 1/2 years of physical presence in the U.S. during the five-year period preceding your naturalization application. And since you've moved home you say you've never been absent from the U.S. for more than six months. But, presumably, your returns here since July of 2007 have been short, work-related stays. So we'll assume that your travel pattern since moving home 19 months ago has consisted of short stays here, and long stretches of time in Ireland. It's going to be hard - not impossible, but hard - to convince the U.S. Citizenship and Immigration Service (USCIS) that you've maintained a primary residence here given that travel history. Another naturalization requirement to very much bear in mind is that applicants must have resided in the state or district where the application is filed for at least three months. As you're currently living in Ireland this would be impossible unless you relocated. Naturalization cases cannot be processed abroad, except for members of the U.S. military. If you were to return here and establish residency you would be eligible to apply for citizenship in July of this year (applicants can file paperwork four years and nine months prior to the five year residency requirement). Again, though, you'd have to prove that your absence since July of 2007 didn't constitute an abandonment of permanent residence. Once you become a U.S. citizen, you would be able to apply for permanent residency for your wife as an immediate relative, which would guarantee a much quicker processing time than applying on her behalf as the spouse of a permanent resident.
POLL: Who won the first presidential debate, Clinton or Trump?