Heiress,
My post of
"Trust yourself. You know more than you think you do." was not to be my pinhead answer to your question. It is what determines the kind of life that we want for ourselves and makes us responsible for ourselves. Trusting yourself is a process that you discover as you grow through life.
One of the ways you can build self trust is by trusting your feelings and hunches. Trust your intuition in life.
You wrote
"He and the girl friend (who I like very much - she doesn't replace my mother but is a nice friend to have) - arrive at my house for festivities with "non-alcoholic" beer for their beverage of choice. I did not plan to serve anything even remotely like alcohol in deference to his condition." "This stuff looks like beer, tastes like beer, smells like beer, and comes in a bottle that looks like a beer bottle." "Would you say that this is a good beverage of choice, given his refusal to go to meetings or counseling of any kind, or am I still in the angry stage of my confrontation of his illness?"
You have your own answer inside of you to your question.
Take a look back into your past life experiences and analyze the reasons why your inner self answered your question the way you answered it that way.
"My dad was forced to stop drinking in June (2010)......" "He was taken to the hospital where they put him on some kind of drug which I guess weaned him off the alcohol......" "He refuses to go to any meetings or go to counseling, because he can 'whip it on his own.'" "He has been a drinker since high school = he's 73 now."
Finally, listen to what your body is saying to you. Be aware of what is going on in your own body. Your body will tell you when you have anger, guilt or resentment built up.
There's an adage in AA that says
"You are powerless over people, things and places".I believe your dad's use of non-alcoholic beverages is like
"dancing with the devil"! 
Just my personal opinion! Take what you like and leave the rest.
Love and Peace,
Phoenix