The most common and most likely answer to this crossword clue is the 5 plus 4 plus 6 letter word WATCH WITH MOTHER
I've seen this crossword clue in The Times
W
A
T
C
H
W
I
T
H
M
O
T
H
E
R
Buddy explains!
The straight part
We know that "Kids TV shows" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kids tv shows = watch with mother.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.