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

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.

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.

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.

One thing that might be happening...anesthesia can have lingering effects in the elderly. It can take months for the brain to get back to “normal”. There can be brain fog, depression, apathy, feelings of disconnection. The brain chemistry has been seriously disturbed. Many surgeons now understand the problem and use more local blocks and less general anesthesia, but it depends on the severity of the injury and surgery. Perhaps the doctor can prescribe some medication, like an antidepressant, to help her over this hump. Depression is common - anyone would be depressed if confined to bed and unable to move without help. A person who’s depressed - even a young healthy person - may not have enough energy to do anything but lie in bed. It’s worth trying to see if medication can help.

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.

You tell mom that you and sister can not move her. If you move her in the wrong way you can injure her again or you or your sister can get hurt.
It is either accept help from the caregiver that you have hired or she goes to a rehab or assisted living facility. Those are her only choices.
The important thing is DO NOT BACK DOWN. If you are there and she has to get up for lunch say I will get Nurse Susan to help you. Then you go get Susan. If mom says "no I want you to help me" all you should do is leave the room.
She probably should have gone to a rehab facility but during these times I understand the concern of being in any facility. the doctor should order Physical and Occupational therapists and mom should comply. Tell mom that if she does not comply with the Therapy you and sister may have no option but to find an Assisted Living facility or hire a live in caregiver. It is just to dangerous for you both to help her. Worst case is mom will get injured as well as both of you.

Seems mom needs to go to a rehab facility. In rehab the staff help her to move safely and she will get PT daily if not several times a day. They can give her pain medications before her PT so she has less pain. She will need to "work" and it will hurt a bit but she will be more mobile.

If mom refuses to go to rehab, she will be depend on others for her mobility. There is equipment you can rent or buy to make that easier for yourself. Ask doctor for PT referral for a home visit. PT can show you how to safely move mom to save your backs. PT can also give the best recommendations for assistive devices and instructions on using whatever you rent/buy.

I don't know if it is just being stubborn, or dementia, or anger from being dependent. She has to have care but if her needs are greatly impacting you and your sister and causing both of you physical harm as well as other problems, YOU must get very tough with her and lay down the rules that are to be obeyed. In her condition and age and behavior, YOU must take charge. If you have a nurse who can and will handle her, then she must be made to understand it is the duty of the nurse to help her and she MUST accept that and that you are physically unable to continue. Tell her she has a choice - do as told or she will be placed - and be prepare to do it. YOU must be firm and tough when they get like this or YOU will be destroyed. Do not let that happen. Good luck.

You tell mom you're back is hurt and this other person in the room is there to help YOU not HER. Both you/sister have a chat with her when she is clear headed: These people get paid to lift/help/rehab you. Do you want to get better or do you want to go to a nursing home where you will probably never walk again?

Keep in mind that pain meds are probably being given to her and they can change her personality. If her behavior changed suddenly, ask them to check her for UTI. Very common problem in facility settings and after surgeries. You'd be surprised how quickly one can return to normal after getting a UTI under control.

Edit: It looks like you have her at home, not rehab. Talk to dr about getting her in rehab. Even if it means taking her to ER (with uncontrolled pain, or whatever reason) and then telling dr to discharge her to rehab. Usually easier to go from hosp to rehab than from home to rehab