Your riddle, if I understand correctly, works on a simple principle, namely two different meanings of the same word. While this is a nice principle, the implementation is, IMHO, a bit weak: there are too few constraints on the desired answer, which broadens the list of possible answers. For example, I can think of at least three other answers, which I believe satisfy all the clues:
Hypothetical Answer 1:
I think the answer is :
Puzzle.
Because:
You may want it here,
We want good puzzles here on PSE.
But if you get it real,
You'd surely want it gone,
For it has no place at home.
Because I don't want to be puzzled in real life.
Hints:
I am hard to get/catch.
Puzzles are hard to get (solve).
You will like me here, you will never want me/like me real.
Explained before.
Hypothetical Answer 2:
Is it
fun?
You may want it here,
I do want to have fun here.
But if you get it real,
You'd surely want it gone,
For it has no place at home.
fun+real=funeral=sad :(
Hypothetical Answer 3:
Maybe it's
gold?
You may want it here,
You want gold badges.
But if you get it real,
You'd surely want it gone,
For it has no place at home.
Because then it might be stolen; you'd keep it in a bank instead.
I'm not saying that was a bad puzzle; I simply want to suggest why it might have been put on hold as "too broad".