I feel for you.
My dad died earlier this year after years of severe dementia and my mum has dropped off a cliff mentally since then, almost as though she'd been holding it together to care for dad.
As you say everybody is different, dad was easy to deal with in that he accepted his position in many ways and, as mum had always run the household anyway, was fine with having decisions taken out his hands and being told he couldn't do things any more.
TBH I don't like my mum much any more, we obviously love her and still try and do the best for her (I'm 1 of 4) but god she makes it hard. Every thing you try and do to help her manage her condition is taken as criticism and she gets belligerent, angry and verbally agressive.
Have you got an official diagnosis of dementia and a lack of capacity? That will help smooth the path to POA and may help with managing your dad.
We took mum's car keys off her because she was dangerous and kept getting lost. Absolute hell broke loose, accusing us of being cruel and vindictive, telling us dad would be disgusted with us, etc.
We finally agreed to give them back if she passed a driving assessment, which she failed. But having a professional outside the family tell her that, rather than us, made her listen to reason and also took the blame away from us and has made it easier to manage her anger.
Edit re: POA, yes getting it in place is easier before diagnosis, but sometimes not possible because of the personality of the person, when I say what I say I mean more from a managing the person perspective than the legal situation.