As Gayot Fow mentioned, it's probably impossible for you to join your wife from landside in the UK. However what you can do is make sure both of you are on the same plane. The easiest way to pull it off is:
Have your wife buy a ticket from Turkey to Ireland via an intermediate airport X
Buy yourself two tickets: one from Ireland to the intermediate X airport and one from X to Ireland (the same leg as the one your wife will be flying on)
Once your wife lands in X, join her at the gate and fly together to Ireland
Possible options for X: Frankfurt, Paris, Amsterdam. Others can be found via flight search engines depending on your dates.