Why does Daisy hope that her daughter will be a 'fool' in The Great Gatsby?
This is going to be an interpretation, because she doesn't really state it directly. Daisy specifically reports after this moment that
"that's the best thing a girl can be in this world... you see, I think everything's terrible now... Everybody thinks so - the most advanced people. And I know. I've been everywhere and seen everything and done everything."
I find this to be the most indicative quotes of the book about the era. Daisy has this hope for her little girl that's rather hopeless. Daisy feels as if she already knows so much about the world, that it is almost better to not know, than to know the terrible truths about man that actually exist. You have to think of what was going on in the 20s and how the extravagance and waste and inhumane treatment of people led to a great downfall. She would rather her daughter just enjoy life (that's so like a flapper) than know of the corruption and evil that exists. We come to find Daisy a character with little moral fortitude herself throughout the book, and hope that she would have wanted more for her daughter.
Tom is cheating on Daisy with Myrtle and Daisy knows that. Tom has relatively public affairs ( Telephone call during dinner) while Daisy tries so hard to be shallow to the extent that she want's her own daughter to be a fool. She wants her daughter to be 'a beautiful little fool' so that her future husband would want her and not leave her for another woman because of her beauty and that even if her husband was to have an affair with another woman, Her daughter would not have to deal with it because if her daughter was a fool she wouldn't be aware of it .
Perhaps because the world in which she will live is one in which a 'fool' can thrive - Gatsby, Daisy and Myrtle in particular are all ingenuous 'fools' in some way but have used this to their advantage(s).