That retired home health care nurse might be looking for work or have his own liability as an EMPLOYEE in mind.
I have a law degree but am not a practicing lawyer, but I don't know of any law that requires a spouse to stay home 24/7 and penalizes them for doing necessary errands. There would be no point in your husband suing you, since your assets are shared. People get charged with neglect but that has to be something worse than someone falling while you're out getting groceries.
You have my sympathy. It does seem like your husband has enough awareness, at least at times, to get around things that he doesn't want to do, like the doctor's appointment. You really need to get a diagnosis before you can apply for most kinds of help.
The only suggestion I can offer that you haven't already gotten is that if your husband was in the military for certain wartime years, the VA will give him money for residential care (and you too, as his survivor, if that happened). My uncle qualified for the correct service in WWII and it's really helping out with the cost of my aunt's memory care.
This is the program: https://www.veteranaid.org/
There are specific "time of war" years. My dad, who was younger than my uncle, was in the navy but not at the right time to qualify.
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How Is Wartime Service Defined?
Congress defines the wartime dates that the VA uses to decide which veterans qualify for benefits like Aid and Attendance:
World War II: December 7, 1941 December 31, 1946
Korean Conflict: June 27, 1950 January 31, 1955
Vietnam Era: February 28, 1961 May 7, 1975, for Veterans who served in the Republic of Vietnam during that period; otherwise August 5, 1964 May 7, 1975
Gulf War: August 2, 1990, through a future date to be set by Presidential proclamation or law (for VA benefits purposes, this time of war is still in effect)