Sasha, I work in a hospital, and this situation is very common. It's a big step for most people to have 'strangers' in their house, and a threat to what they perceive as their independence (your Mum will unfortunately not be regarded as interfering with this, despite all the hours she's putting in). As Puss suggests, maybe tell her it needs to be on a trial period, as your Mum needs a break. Tell Gran that if the situation continues as it is, your Mum may well become ill, and that family carers need a break.
Hope Gran is claiming Attendance Allowance if you're putting in all these hours.
Take care