To put it in his own words, what he had written in the first tree was "lost in the senile fog of [his] recollection processes", and he had to work backwards from rereading the reference he had made to the Duck's family in his own stories. As the stories actually didn't follow what Barks had decided for the first tree, this accidentally ended up making the second tree more accurate to the stories than the original one was
This version of the tree,features Scrooge McDuck, a sister of his who married a son of Grandma Duck, Donald Duck, his sister, Huey, Dewey and Louie Duck, Grandma Duck, a daughter of hers who married a Goose and hatched Gus Goose, and another daughter who married a Gander and became the mother of Gladstone Gander. No names are given for relatives not featured in stories.
Interestingly, the tree says that the various mothers "hatched" their children, confirming that in Carl Barks's mind, Anthropomorphic Ducks do lay eggs (a position with which Don Rosa notoriously disagrees).
Behind the scenes
Created for a letter sent by Carl Barks to Don Rosa on March the 31st, 1991, accompanied by this statement “My records are lost and my memory is defunct. About whether Goosetave or Goosetail was the name I gave to the gander who married Uncle Scrooge's sister is lost, too, in the senile fog of my recollection processes. I will vote for Goosetave. It sounds more North European, the natural home latitudes of ducks and geese.”
The letter was later printed in Uncle Scrooge Adventures #42.