Could I alone be caregiver to Alz mom who weighs 30lbs more than me, fully incontinent, in wheelchair and can't get up or stand?

When my mom reached the point where I began to consider buying a lift was also when I realized that I couldn't possibly add another level of care to the already high burden I was under. Rather than tackle this I'm going to suggest you figure out a way to make your mother's care in the nursing home more acceptable.
Consider that her mental stimulation will likely be even lower in your home than in the nursing home simply because she will be exposed to less people, plus all possibility of attending even the limited entertainment available in NH will be lost.
Her primary caregiver (you) will need to perform no matter how tired, angry, sad, ill, burned out without the possibility of relief - in a facility there are multiple hands available in 3 shifts so even when someone is having a bad day (or is less than competent) you can be assured it's not forever, someone new will be available to take over.
Meals are always a problem in congregate settings, in order to make food suitable for the majority they please no one. "Healthier" food isn't really a consideration at this point in life, nothing she eats is going to significantly change her underlying health in the few years remaining to her. If she would enjoy certain special foods that aren't available in her NH you can always prep them at home and share them with her there.
Plus as loving and careful as you are you can never replace the 24/7 availability of nurses who know and understand geriatric care and can spot and treat problems a layperson would miss. You won't be able to provide things like a real bath (the spa tub was a very popular feature at my mom's nursing home). You won't have a dietitian to evaluate her meals, or a doctor to make house calls. You will be the one cleaning up urine, feces, and blood - can you handle that?
And one more thing - it seems like we always go into this thinking the end is near, but I know first hand that people can live much longer than you might imagine with extreme physical and cognitive limitations - think in terms of years, not months.

If the nursing facility says she is a two-person transfer, take their word for it on that.
I was an in-home caregiver for almost 25 years and worked for all kinds of people. Having to move and transfer any sized adult on your own when they are dead weight is going to wreck your body after a while. It makes zero difference what size the caregiver is.
I've cared for more client than I can remember over the years. I can count on one hand how many had family members in the house who would assist with transfers and toileting.
Sure, it's possible to care for a person ailing with Alzheimer's who has to also be lifted and transferred from point 'A' to point 'B' and toileted several times a day the same way on your own.
The first thing that will go on you will be your hands. The pain will start off small at first. Then you'll maybe start putting on hand braces like I did when it's time to move them or reposition. Then it's wrists. Then your shoulders (usually a worn out rotor cuffs). Then your knees from your legs taking all the weight. And of course, no matter how careful you are or how good your practice of body mechanics is, your back goes.
I couldn't do hands-on care anymore even if I wanted to which I most emphatically do not.
Do not move your mother into your house. Maybe in the nursing home she can be toileted with an assist of one. That will change. Be a good advocate for her instead if hr hands-on caregiver.

No you will not be able to care for her at home. My father tried to care for my mother who needed two people and had never ending issues including many falls. It is dangerous, especially if you aren't trained.

You are planning to pay for hours of outside help? What happens when she declines and needs more and more help?

Who else is in your home (you write "we")? And what do they think about it?

There is no way I'd risk my physical health so mom has more mental stimulation and gets better cooking.

What happens when you injure yourself lifting her?

Are you the only one making this decision? Do you have siblings?

No.

Your mother is in a NH for a reason. She needs 24/7 care. A MC is limited to what they are capable of. I am sure if Mom became a 2 person assist, they would have told you she needs more care than they can give. IMO MC is just a step up from AL the difference, its locked down and may have more aides.

My Mom was the same weight I am and I could not lift her if she fell its dead weight if they can't help. Many a time I tried to help her out of her chair and she pulled back and I let her go back into the recliner. I was not putting my back out.

I agree willey about interaction. My mom had no socialization, it was just me. She no longer could read, she nor I did puzzles or like to play games. She sat and watched TV. At the AL, she had freedom to walk the building. She was in the Common area most of the day so she had socialization and entertainment. Lots better than living with me. Even at the NH they knew she was happier among people even if she could not always participate in activities.

Guess I question why you would consider doing this? If she is in a nursing facility with trained staff members and proper equipment what is the reason you are even considering this?

There is no way in the world I would consider this, I would leave her where she needs to be. Certainly not in my home or anyone else's. She requires way too much care for a lay person and she will continue to get worse, there is no better.

I have ruptured a disk in my back. Trust me, you don't want to go there. It pushed childbirth WAY down the list on The Worst Pain I've Ever Experienced. (To be fair, pancreatitis pushed a blown disk way down that list, too.)

I think you can find better options to deal with the food issue than bringing her home. Sometimes there is no ideal situation, but the best possible situation for the moment. What would happen to her when you blow out your back the second week she was home?

Peanut,
If this were not your Mom, would you be thinking that this caregiving for an Alzheimer's patient heavier than you was a job you could be doing?

It is not sustainable.
This level of care cannot be done by one person without further stressing the caregiver who is healthy, let alone someone who has any back problems.

Will you have caregiving help to cover 24/7 care for 3 shifts per day? How many "shifts" do you feel one person can take on?

I hope you will make good decisions for your Mom to get the care she needs.
But am more concerned about your health right now.

"I think the real question is why would you want to?" as sp19690 asked.

Ask WHY then REALLY unpack those reasons.
Can alternative means meet those wants/wishes intead?

Eg
Q. Because it is right to care for one's parent?
Unpack: What is 'right'? What is 'care'? Is it physical care or emotional support? Must 100% care be provided by your own two hands? Is arranging the care, being the co-ordinator or advocate still caring?
A. Setting up a realistic & safe care plan with adequate caregivers IS care.

Q. Mom wants to live with family?
Unpack: the expectation of living with family can be a sweet idea... Nanna rocking on the porch.. The reality can be a stress-out, burning out solo caregiver, injuring themself while the elder is still unhappy/bored/wants to go home.
A. appropriate care to enable needs to be met + located close to family to enable frequent family visits.

Q. Because generations before cared for their folks?
Unpack: Compare apples with apples. Caring for fully mobile slightly older folk with low health needs is very different to caring for folk with mobility, behavioural, emotional, physical health needs.
A. While the past DOES shape our values, it cannot decide the future. Decisions today must be based on what resources are available today.

I am but one person. It is ok to say so.