What does your mom say? After all, she's his wife. When my mom cared for my dad during his fatal battle with cancer, I took no issues with her approach, but did learn from it and the mistakes she made, especially in dealing with the medical community.
Many of the other aspects depend on what state you live in. Hard to give blanket advice.
As Lynne said, a medical professional will determine that NH care is necessary. You can, however, place your father in assisted living (in a facility that has dementia care) on your own, at your expense. You also can assess NH in your area and determine which would suit your needs for a prospective placement and communicate your preference to his doctors. Also, ask for their opinion and that of their staff. Use the online Medicare NH comparator to find out more information.
Best wishes!
Pat