Daisy is cute, in the way a little furry puppy is cute, or a baby in a sunbonnet or a little old lady with bright pink sneakers. Meaning, yeah, it does seem immature.
Daisy Lillian is just too flowery, like
Rose should be tacked on after
Lillian.
I think
Marguerite is a beautiful name on its own. I agree that using
Daisy as a nn for
Margaret or
Marguerite is far-fetched. Also pretentious.