Recover Chair Seat - Should be easy, right?

I try very hard to re-use things and to make things that can be re-used or recovered easily. I bought a pair of folding chairs from Target that are pretty comfortable and cute, but the seat was covered with a black vinyl that started to tear.

This is Piper on the better chair which I have yet not recovered.

This is the vinyl that I took off of the worst chair. You can see why I needed to recover it. Fuzz Parker is in the background nesting on my batting. You know you can't keep a cat off quilt batting.

Here's the photo of the recovered chair. Looks pretty good, doesn't it?

Except that when I removed the bottom (forcefully by hammering on the underside) I broke the rabbet which held the seat in place. I didn't realize that the seat was rabbeted in. I think I can get John to help me glue it and tack it back on. I will have to cut the rabbet off on the other seat to get that one out.