She wants to go home and I want her to go home, but this will cause a family fight. Any suggestions?

YOU are her POA. YOU were appointed because either you are THERE or you are most COMPETENT or both. You are to act FOR HER. No one else matters in this equation. It is now on you to evaluate, with her MD, if she can be safe with in home care, or if she cannot. If she goes home and it turns out she needs to return to care then you can have her return to care. If she is evaluated and competent then you don't even figure in the equation, and it is SOLELY HER OWN CHOICE. You need simply to leave "the rest of the family" out of the equation. A simple "Mom's doctor evaluated her; he feels she can return home. I am fulfilling my duty to help her act for herself; if this doesn't work out we will re-evaluate. Sorry, but I have no time for argument on the issue."
PERIOD. It is time now to cut out the extraneous fat in the issue. Good luck! Update us if you get a chance with a "Mom's Evaluation" note; I am curious how this will work out for you and Mom. Again, wishing you the best of luck as you fight for what is best for Mom. Remember, her safety is paramount.
As to not liking Assisted Living or other facilities, do let me know when you find ANY senior who does. End of life stuff isn't always about "liking". It can be an impossibility. Hugs to you.

What is her diagnosis? Why did her family place her in AL? If she has short term memory issues, it's not likely safe for her to be left alone. She could start fire, mistake medication, etc. What would hiring 24/7 care in the home costs?

If she has cognitive decline or dementia, it will likely progress and she'll need increasing amounts of assistance. An assessment should be able to tell what level of care she needs. That is, if they had the right information to complete it. My LO would say that she was fine at home, that she could bathe herself, prepare meals, take meds, do laundry, but, none of that was true. She was not aware of just how poor her abilities were. Sometimes, short term memory issues come along with decreases in proper judgment, so, that things like safety measures, using walker, not opening door to strangers, etc. goes downhill.

I'd likely read a lot of posts on boards like this. You might also spend a full day with her, so you can see just what she is needing. A short visit may not reveal the full picture. The person may not be the best one to determine where they are safest. Nursing homes are really designed for those who need nursing care. Maybe, you could find a good fit for her needs. I read a lot about family members with good intentions who don't realize just how much help the LO needs, until they get back home and it becomes abundantly clear. There's a lot of that around this site.

We need more information. What does "go home" mean, as in would she live by herself in her own home? Apartment? Or would she go to live with a relative (you?)?

Are you local?