My family just went through this a couple of weeks ago and my heart goes out to your family.
My Dad is 86 (day after tomorrow) and developed Sudden Onset Dementia about 6 weeks ago. Without his medication he is delusional, (sees and talks to my grandfather who died 44 years ago, for instance) has bizarre hallucinations, (saw my 10 year old nephew flying outside his 4th floor hospital window and to this day will not accept it didn't happen) and cannot control his behavior (he hit the nurses several times in the hospital and had to be physically restrained and sedated.)
He is also dying from kidney failure, and we just found out yesterday he has a UTI. He takes meds for diabetes, his kidneys, high blood pressure, blood thinners, antibiotics much of the time, his dementia medicine, and it changes every few days so is a bear to stay on top of.
We initially were told he was too ill and required too much care for the family to provide, and would need to be placed in a nursing facility. We were looking into placing him and Mom together. Then 2 weeks ago yesterday (insurance was running out) when my sister went to see him she was told that he would be sent home that Friday, and it was a big surprise to us all. My sister and BIL took two 1-hour training classes, were shown how they would need to care for him, and a shower bench was delivered so he can shower more easily.
He cannot do anything for himself other than go to the bathroom, and he makes a mess doing that so we are cleaning up after him. He can dress himself with help. He wets the bed (even though he wears diapers) so it's changed every morning, we take turns fixing meals for him and Mom, (who has health problems of her own and cannot help) and our house has been consistently filled with a social worker, home health nurses, physical therapists and occupational therapists these last almost 2 weeks.
Everyone but the social worker (who can come whenever she feels it's necessary) will cease coming at the end of next week, so we will truly be on our own. I have fibromyalgia and a 27 month old, my sister has diverticulitis, my BIL works 12+ hour days...and realistically we think the time to place Dad in a nursing facility will come quickly, because while yes, there are several of us who share a home with him and my 78 year old mother, it is HARD to care for him.
He has always been a stubborn man, but now with the dementia he is many, many times worse. He is also very highly and easily agitated over the tiniest things, right now he is angry because he thinks his home health nurse just walked in the house this morning because he didn't see us let her in. We've told him we let her in, and that we know her (she's been caring for Dad off and on for about 2 years) so if she did just walk in that would be OK, but he is very mad and won't let it go. He will do this all day, and no meds are able to help with it. And, he requires 24-hour observation as he "forgets" to breathe, and someone needs to tell him to when he stops, especially when sleeping. With dementia a person loses cognitive ability, and while breathing is an involuntary action, he forgets sometimes.
So, my concerns for your situation are: 1) IF your Grandfather refuses medication for his dementia he will decline quite rapidly, we were told this by Dad's doctors, 2) If he falls can your Grandmother pick him up, probably not. Dad fell about 8 weeks ago on the side of the house, and my over 6 foot and BIG (muscular) brother had the most difficult time picking him up under his arms. It's because when you try to pick up dead weight it is like picking up 2.5 to 3 times that amount of weight, and my Dad weighed 239 at the time. We have been told not to attempt to help him up but to call 9-1-1. 3) I realize your Grandmother wants him home, so did my Mom, but can she really do all that will be expected of her? She will need to fix his meals, possibly at some point help him to eat, clean up after him, keep the house clean, possibly change diapers at some point, give him and get him to take his meds consistently as it's extremely important he takes them regularly and on time, and be alert and proactive to possible changes in his demeanor (the dementia or threats of suicide) and his body (will she recognize the need for him to see a doctor or go to the ER if something is wrong?) What if he hits her or wanders away while she's in the bathroom? He has dementia, it IS a real possibility. And she has to still care for herself, eat right, possibly do grocery shopping, etc.
Dementia only slows down with medication, it doesn't stop, and will get worse as time goes on, these are all things to consider. It is a HUGE responsibility for anyone to take on, and I don't believe if I was a healthy 79 year old I could provide the care required.
If he stays at home make sure you get him a bracelet to wear at all times that lets everyone know he has dementia and has contact information for your mother AND another family member so so someone else is aware. Keep in close contact with your Grandmother to monitor any changes in her health, it is a fact that caregivers are under lots of stress and their health can suddenly decline. Ask the hospital what items you should have in the home that will make things easier for your Grandfather to function, such as a porta-potty, shower bench, locks they can recommend for the doors, etc.
God bless you and your family, I pray that He will guide your decisions❤