I use those kind of hoops for framing and stitching. And sometimes after international shipping some of them come broken, it's because inner part was made this way and it's sensitive for pressure. But I don't throw them away, they can be easily fixed.
I use regular glue for paper (in Ukraine it's ПВА, it's white glue which becomes transparent when dry) it's going to work great for wood as well. To make it stick together for a while till glue will dry I use washing tongs and leave it for one day. Next day you can take it off and use your hoop.
Note: take off outside hoop and dry the inner hoop separately ;) so they will not stick together.
Hope it's helpful 😉