The most common and most likely answer to this crossword clue is the 6 plus 2 plus 9 letter word SPHERE OF INFLUENCE
I've seen this crossword clue in The Times
S
P
H
E
R
E
O
F
I
N
F
L
U
E
N
C
E
Buddy explains!
The straight part
We know that "Swingball in one’s backyard?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case swingball in one’s backyard? = sphere of influence.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.