This is such a brutal time of life, for you and your parents.
So many things about elder care, aging, and nursing homes do not look like I thought they would. It sounds like your father still has a lot of physical strength, which also complicates things. I never knew so many old people could be so strong, not when caring for them and thinking about HOW to care for them makes me so tired and weak.
I am glad you have found a support group. Have you read the AgingCare forums? Those have been very helpful when I have questions, particularly about drugs that care facilities suggest when people with dementia are agitated.
There are no good answers. You can only do what you can do. I am wishing you the best.