Basically what deciphers where you are taxable is your residency, ordinary resident and domicile status. Based on these, it determines how your income is taxed in Ireland.
The residency & ord. residency are defined in Tax legislation - boils down to where you are located & for how of the year....based on the time you have said....she would be still considered to be res, ord res & dom in ireland----taxed in ireland
and if your wife was not paying tax here......she may be likely, as suggested before, to pay tax elsewhere (where rates maybe higher/lower)...so its not a case of getting out of a loop