Curiousdan you have actually become your fathers unpaid carer. There are hundreds of people doing what you do voluntarily every day, some get carers allowance some don’t. However most of them do it because their loved one is ill, frail or immobilised. We all have a choice although is is extremely hard when it concerns a loved one.
If you are working on top of running two homes you will grind yourself in to the ground, if you are not but married your marriage will definitely suffer.
Write down what makes you crabby and why, you can’t change your dad, it sounds like he has always been like this. Losing your mother has made him lose interest in life after so many years of doing very little together. When we get to the late 80s/90s our bodies start to slowly close down, particularly if we are not active nor engaged with anything stimulating. This is was is happening to your dad and HE is not worried about that you are.
I would have a calm conversation with him, saying that you are exhausted and can no longer clean,shop, nor walk the dog for him, what would he like to do about it. Then stick to it and see what happens. Naturally you will still visit once or twice a week offer to take him out, offer him food and chats, but if that is declined leave it, there will soon come a time when he has to have some help. Have you got both POAs you are going to need them. Good luck with whatever you decide to do, I really emphasise with how difficult this is for you.