this isn't an all-or-nothing choice, if that helps at all. you actually have 3 choices -- nursing home, your home and small care home that might offer the care your mother needs.
also, should you have your mother home, let Hospice be part of the picture. you would get great help from them, including actual people help. i believe, just by her health conditions, your mother would be eligible.
find out whether her Medicare plan allows paid help (contact your local senior services), or whether your state pays family members. then you can also hire in helpers -- and you should. your mother's care is not a one-person job.
if you choose nursing or care home, read the inspection reports (they must show you, by law) and you'll get to know their issues and strengths.
You can still have your mother home for visits even if you choose nursing home care. or you can choose respite relief care in a nursing home when you need a break.
my own favorite choice for dementia care is the small care home with up to 6 residents. check those out in your area. it's the best and most supportive care, if other major medical issues don't need nursing. nursing homes are never the best choice for people with dementia. they don't need nursing for dementia, they need companion care. small care home welcome family visitors.
so talk it over with senior services, go to one or two support groups and get mutual help, support and information. Then decide.
please don't dismiss care staff. i've worked in the field for 20 years and it's amazing the love and caring among them. when it isn't, it's usually because they're underpaid, over-worked and not being appreciated. don't make any assumptions -- do your homework, think it through and you'll know what you want. and don't forget the mix-and-match approach.