How can I make the doctor at the NH (where mom is) order another CT scan?

Roberta, it sounds as though your mother is declining rapidly, and you want to know why. Does the" why "matter? Given the long list of her physical ailments, it could be any one of them or a combination. None of them is curable. If she's having more stroke symptoms, what treatment would you seek?

Try to look at this as "what can we do to make mom comfortable , non anxious and pain free". Does that make sense? Do you want your mom subjected to more machines, needle pricks and tubes? If you do, that's what an ER will do; call 911 and you'll probably get what you want. But if you want peace and comfort for mom, leave things be or ask about hospice. I wish you peace of mind and clarity in making tough choices.

If Mom did have a CT scan, how would that improve her life? If you could say without any hesitation, "See, she did have another stroke," how would that change the kind of care she is getting/needs?

I don't know why the doctor will not order one. But I'm more interested in why you think it is important.

You can't fix your dear mother at this point. You can see that her symptoms are treated and minimized. You can insist she be kept comfortable. But with or without an image of her brain, she is going downhill.

Are you considering Hospice care for her? Would the doctor approve that at this point in time?

Before you look for something, you need to be clear about what you plan to do if you find it. If you are anxious that your mother might be vulnerable to further strokes, and she isn't already on medication to help prevent this, you could try asking her doctors to consider it. Don't get into a wrangle about one type of investigation at the expense of getting them to review her treatment overall.

By the way, I am told that CT scans in brain injury are at their most useful when they disclose a bleed rather than a clot - and a bleed shows up like a lit Christmas tree, straight away. Other than that, it may be just as useful to be guided by symptoms - do you feel that the NH is ignoring your concerns about how your mother is in general?

CT scans and MRI's have to be approved by an insurance company, and many will not approve that kind of imaging unless you are rolled into the ER.
We are going through the same thing. Mom gets to the ER but refuses to stay overnight and wants to go home. We are certain there is more stroke activity.
At this point her vascular dementia has progressed to the point where she cannot remember how to use the telephone.
So we are filling out a MOLST form (Medical Orders for Life Sustaining Treatment). You can opt for DNR yes or no, along with feeding tubes, oxygen, respirators, etc. in accordance with her wishes.
Sorry to see you are in the same boat.