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.
The mother's right over her son is indeed great, and obeying her in whatever is lawful and good is one of the strongest obligations. However, you are not obliged to obey your mother in divorcing your wife for the mentioned reason. Rather, you should not obey her in this regard. For more benefit, please refer to fatwa 84056.
There is no harm on you in moving your wife to a separate accommodation away from your mother. One of the rights of the wife over her husband is to provide her with a suitable, independent accommodation. Please refer to fatwa 84608.
So keep your wife, live with her in kindness and rejoice at the divine blessings that you shall receive by showing kindness towards her. Hopefully, Allaah would bless her with perfect recovery and bless you with righteous children from her.
Allaah knows best.