Along with this forum, we have a system of senior centers in my area (Salt Lake County, Utah).
Do you live anywhere near a town that has a senior center? Sometimes, the folks at the senior centers can provide help directly or can refer you to places that can help with the counseling side of dealing with an aging parent.
I guess my Dad and step-Mom made it all look so easy. They both always expressed their appreciation for our help and visits right up to the end. Their need for our help only got serious during the last 3 or 4 years, during which they were still living in the familiar surrounding of their home.
Dad passed away a few months after his 100th birthday and my step-Mom of 26 years passed away at age 92 just a few months later.
My brother and I had only a small taste of what you have described with a just a few years of trading off 2-day stretches of staying with and helping my parents. Ours was still more positive. We were invited back any time either of my parents thought to include that in the good-byes, but it was never a backhanded invitation. My other three siblings gathered round from their various states of residence during the last few weeks to months to help. Two of my step-sisters also alternated taking my step-Mom home with them to each of their other counties for a short 2- or 3-day visit from time to time.
Whether from this forum or from other sources, I hope you can get the help you need to regain your equilibrium so you can share emotional support with your Dad.
Stay well.
-Lynn