I am writing a piece explaining I am not a great-great-grandmother, but a great, great-grandmother. I believe the comma is needed in great, great-grandmother to show an opinion, then the age. Is this correct?
No. great is an adjective. great-grandmother is a noun.
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No.
great is an adjective.
great-grandmother is a noun.
You don't put a comma between an adjective and a noun.
You could say 'terrific' instead of 'great', to avoid confusion.