Sorry about the lack of help on this one. Treated wood would outlast the kids so it wouldn't be worth it except for a playground or a series of kids.
We bought a plastic turtle sand box with cover for our daughter, she used it some for a short period but mostly it just has sit there. What a waste of money.
When I grew up, we couldn't afford our own sandbox. Just used the one at the school playground with regular 2x8 sides and road sand/gravel inside. Didn't worry about cats or covers. Just tossed it aside. Of course that was back when I walked 2 miles to school in blizzards with 12 inches of snow, etc.