Sv: "Klä om" sadel
Bruce Grant's book "How to Make Cowboy Horse Gear" has a section in the rear by Lee M. Rice "How to Make a Western Saddle." It doesn't say much about attaching the wool to the skirts, but here's what it has. This is done after the seat is made but before fitting the jockeys and fenders.
You are now ready to put the skirts on permanently. First, after the woolskins have been pasted on and sewn, trim and edge both the skirt and the woolskin and polish the edges. Lace together at the back. Be sure lacing will be covered by the back jockeys.
It continues with more assembly instructions related to attaching the skirts and adding saddle strings.
So it sounds like you need to both glue them together AND sew the edges. You can probably saddle stitch it by hand (requires two saddlers needles [not sharp] and good strong thread, such as waxed linen) using the pre-existing stitching holes. You probably also need an awl to make the holes in the woolskin if you use real skin.
I've never had this problem so haven't tried it myself, but that's probably what I'd do if I did. I'd use rubber cement (klebfast or other types sold for leather working) to glue the skin on. You put it on both pieces, put them together damp then pull them apart. Then give the glue a few moments to get tacky and put it back together. Holds better that way. I would probably also consider pulling the rear lacing out and relacing it afterwards, if it is accessible enough to do so. The lacing probably helps keep it in place at the rear and it is not possible to sew through the existing lacing. Adding a row of stitches outside the lacing would probably look pretty ugly. Plus it can be really difficult to make new holes in the skirts, especially if you don't have the proper tools for it. Might need a new strip of latigo or other leather to relace it. Would have to study the lacing method carefully to be able to duplicate it. I definitely wouldn't trust glue alone to make it hold.
I haven't sewn on new skins, but I have redone stitching in old saddles where it had been worn off by the fenders and girth straps. In this case the saddle had in-the-skirts rigging, making the stitching especially important. Making good even stitches takes practice and time.
If the saddle is in top condition otherwise, you may want to consider finding someone with experience to do the work, even if it means sending it out of the country.
(Wrote in English since I figured that was easier in this case. Am happy to explain in Danish if preferred.)
