It gets a lot more complicated when you apply through a minor or other dependent. You have to have sufficient resources to support yourself and health insurance. If your child is of school age, they need to be enrolled in school before your wife is eligible to live in Ireland, as far as I am aware.
I would advise you to read the Directive regarding the free movement of people in the EU
and read the relevant parts thoroughly.
It has been a long time since we attempted an EU treaty rights application so I am afraid I cannot advise you too much as I simply do not remember.
beloved is the enemy of freedom, and deserves to be met head-on and stamped out - Pierre Berton