The second comma before “and” is optional, isn’t it? I usually use it, but left it off this time. It’s probably better with it for precise clarity.
Your comma is correct. It does make a difference whether or not you put it there though.
For example:
“eats, shoots and leaves” means exactly what you think.
“eats, shoots (like a gun), and leaves (exits the area).
Brits do not add a comma after and, but in American English, we do. (which I don’t understand why the Brits don’t..)
The comma placement changes the whole meaning.
Oops.. minor correction (mistake on my part) (yours is still correct):
“eats shoots and leaves” is correct for the expected meaning.