I am very sorry that your Mum is so unwell, and you and your family have my good wishes during this worrying time/
The problem seems to be that your Mum cannot get rid of her high levels co2, and that means that her o2 levels must be too low when she is off the ventilator. Giving more oxygen will not be the answer, because as her o2 level rises her co2 level will rise higher. I wonder if your Mum has any pre-existing respiratory condition that would account for this development post surgery? Also, I wonder if the ITU or the chest team at your hospital provide any form of non invasive ventilation? This type of ventilatory support is used successfully in many chest units for many patients who have this type of respiratory failure. It involves a mask and a small ventilator, and the patient uses it for short periods during the day, and for several hours at night for as long as necessary until the co2 and o2 levels are steady.
Patients with pre-existing chest conditions have many problems coming off ventilation with a tube - endotracheal or trachy.