I support the suggestion for using Gorilla Glue which, yes you need to use correctly but it is by far the best wood glue. I use only it in working on wood repairs - years ago I put together a set of chairs which had been previously repaired using the standard PVA glue (which I scraped off the parted surfaces) and the decision had been made of giving up. The chairs are still intact. But make certain you set things correctly - you won't get them apart for a second try (it sets pretty quickly).