How can I help my mother of 80 something to accept help from her home nurse?

Don't risk ruining your back. Take care of yourself first! Let professionals do it and too bad what mom wants. Back off. Don't be there when nurses need to help her.

I agree with all here who say that she is not going to allow help until she is basically forced too. Tell her that the doctor told you and your sister you need a week of bedrest for your backs. Your mother will be pissed but she will not die and she will have to allow help. You really need to not be there for a few days. Why are you moving her anyway? She broke her hip, not her neck. You don't say how long ago this was. Did she go to rehab? You hired a nurse? A nurse who is letting her get away with this? Does she have care 24/7 or does she live with one of you.

She should be working with a therapist to teach her to get up and walk; or else she will be in wheelchair forever. If she did not go to rehab for therapy, she should qualify for therapy at home at least initially. My MIL had severe dementia when she broke her hip and she could never figure out how to use walker so she had to be in wheelchair.

Personality change is common after something like this type of fracture, but also, you might consider having her checked for UTI. In the elderly, they often don't have symptoms of burning or urgency but they have personality changes.

My home is my “cave”, my last chance to escape the world
and “hold up.”
i have had to relinquish much of my “cave” due to family members aging and/or having health problems.
I dread the day when strangers potentially come for me.
Can you give your mother a real or imaginary “safe place” of some kind?
I read about a mother of many kids who was able to make a safe place by pulling her apron over her head. Every one knew to leave her alone.
Maybe something like that would help your mom tolerate the nurses and therapists etc for a period of time . Her code to be left alone when the “ help” overwhelms her ?

You are enabling the behavior, so she won't change. Why should she. She wants you two to do it, and you are doing it. But what happens when you are permanently injured?
Did Mom go to rehab? If not, why not? Does Mom live with you?
If you Mom currently will not allow the participation of the nurse sit with Mom, Sis, Nurse and yourself and tell her "Mom, we can't do this anymore. Our backs are going out. If that happens you will be in care in one second. And Mom, do understand, if you cannot cooperate with a nurse sent to help you, then you will need to go to rehab, snf or other placement to get care, because we can't do it anymore. We understand you are hurting, exhausted and in fear over all this, likely depressed as well. We are sorry about that. And if you have to move into care we will grieve that, but there is honestly nothing we can do about these facts."
Protect yourselves. No one will do it for you.

It will take you backing off for her to accept help. My dad desperately didn’t want anyone in his home, but came to accept and even cherish his helper after we backed off. The helper was also excellent at winning him over, as many people who do this for a living are, having developed skills and tricks of the trade in working with seniors.

In your shoes, I would tell mom that I am no longer coming over to "help" each day because her care needs are for a medical professional, not an untrained daughter.

Visit, but don't help. If mom needs re-positioning, you step away and tell her that your doctor has ordered you to not do any more lifting.

Why would you and your sister risk life-altering injury to care for your mother when there is a nurse at her bedside?

Her wants do not outweigh your NEEDS.