There is no scene where it is said that Anthony is seeing a psychiatrist.
None.
It is not even hinted at.
All Kay says is "look at your son."
Michael says "Anthony's fine."
I have the five disc DVD set and the very rare fan assembled 588 minute set of the three films.
I know them all pretty much verbatim.
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Fredo was involved in a plot to kill Michael. How much he knew is debatable.
"You guys lied to me. Don't call me again." - Fredo, in bed, and on the phone after the Michael assassination attempt.
It was Johnny Olla calling him.
Having said that, he still deserved to die. If one of my brothers tried to kill me and failed, I would most definitely kill him without hesitation.
Michael does the right thing in waiting for his mother to die first.
If Fredo had any sense of honor, or of manhood, he would have killed himself like Frankie "Five Angels" Pentangeli did.