The most common and most likely answer to this crossword clue is the 6 letter word WIDDLE
I've seen this crossword clue in Independent
W
I
D
D
L
E
Buddy explains!

The straight part
We know that "daughter is into Wilde, surprisingly (6)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case daughter is into wilde, surprisingly (6) = widdle.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
Crossword Answer definitions
WIDDLE noun- Urine.
- An act of urination.
- To urinate.
- To play guitar (especially the electric guitar) quickly.
- Little.