@OurLass, if no one has said, hello and welcome to Talking Point, please allow me to say it. I hope you will find it welcoming and helpful here.
I am very sorry to hear about your mother, especially her recent fall and hip fracture, and all the worry and stress you have had.
I am in the States and things work differently here, so apologies in advance if I say something not applicable in the UK (if that is where you are), or something downright stupid.
I hold Power of Attorney for my mother (dementia, in a care home) which allows me to make decisions about finances and health care, among other things. So in your situation, I could refuse testing like the CT scan, or a hospital admission, or so on. I gether that is not always the case in the UK but could you have some frank discussion with the persons in charge, to let them know how you want your mother's care to go? So often in caring for someone with dementia or other illnesses, we reach a point where automatically treating or diagnosing everything, is no longer in their best interests.
I hope one of the experienced UK members can better advise what I have not terribly clearly tried to suggest.
Very best wishes to you and your family.