Hi,
Not sure what you mean by full tax.
For example, if the house is in joint names and you earn €10,000 net rental (after expenses & restricted mortgage interest), there will be €5,000 attributed to both of you. Assuming your employment income is €45,400+, you will be able to increase the standard rate band by €5,000 (plus you wife's employment income until she stops working, to a maximum increase of €27,400).
In comparision if the house was in your wifes name solely, the increase would be €10,000.
It is not difficult to transfer the property to your wife's name and there will be no tax implications. The solicitors fees should be small enough. However, as I said before if there is a mortgage on the property, they may not allow the property in a sole name without some rejigging of the paperwork. Not my area of expertise though so someone else will have to help you out there.
I do know from personal experience that it is possible, I think (again not 100% sure) that you would have to sign something and get independent legal advice that you are aware and understand that you have a responsibility for the mortgage but no legal right to the property. This is what happened when I bought my house and my dad co-signed the mortgage but he is not on the title deeds.