Tango is allowed in our inflatable pool, but only when she's just had her nails done. When she was younger she had her own pool with a liner in it and she got a couple of holes in it, even with really short nails. Now she has a plastic one. It's not very deep, but it works and she likes it.
That being said, the one in your link looks more durable than the one we had. I'm sure it would be fine. If he does tear the liner, it isn't a huge deal as it doesn't wreck the actual pool and you could always patch it up.
Bookmarks