All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If this house is your own property and you have registered it in your mother's name temporarily, merely on paper, with the intention to transfer its ownership later to your name, then you have the right to do so, and you may also offer the house as a gift to your mother or to anyone else. As for your wife's suggestion to register the house in your name to preserve your right to it, then you may act upon it if you wish. This does not conflict with allowing your mother to stay in the house for the rest of her life.
On the other hand, if your wife has contributed to the building of the house and she is a co-owner, then she is entitled to her share and has the right to request registering her share in her name or the name of whoever she wishes, and you are obliged to fulfill her request in this regard.
In any case, we advise you to register the house in your name so as to avoid potential disputes and to preserve your rights. This does not conflict with dutifulness towards your mother, and it does not mean that you cannot leave the house for her to live in it for as long as she lives.