Hi Jamie,
Thanks for the file, so much better to answer this. I opened it and it looked already like a problem file. Perfect example! Great share! So, lets inspect this. (I have recorded some steps, see the link below) Some ideas or suggestions might be not really working here, but perhaps they are worth mentioning for other projects.
The first thing that I always do, when a problem is given, checking the mesh.
Typically the Normals, especially in 3rd party models, are off. Same here.
Normally you can fix this quickly with the Mesh>Normals> [see options]
The second part is to check the polygons itself. Are they OK, connected, or even un-usable, etc?
In R17 we have now a new tool for that: Mesh>Commands>Modeling Settings. Problem areas become faster visible.
If there is a quick fix is certainly a longer discussion …
In UV-Edit, the first idea would be the UV Peeler, but the “holes” in the given model will prevent that.
The Island problem, is given when there is no option to un-wrap it. An island is a certain amount of connected UV Polygons. If you take a plane object then you can easily predict where the coast of that island is. If you take a sphere, then you have no “natural” coast/beach. An example would be like peeling an orange, you need to break the peel at one point to do that, and that break must be large enough. So, speaking of UV peeling we need to introduce a cut/seam, so we get a “coast” to that island. In the Relax part of the UV Mapping>Relax UV you find an option to use an “Edge Selection” to specify this cut. Tutorials are available for this procedure. Edge Selections for all the holes might be not really a nice work to do, thought.
If you get an error, and the mesh is OK, and the mesh can be peeled, then select half of the mesh, relax it, no problem, then it is in the other half. Select a half of this and so on. You might be surprised how fast to get to the problem in this way.
Given the Curtain as the example file, what would I do?
https://www.amazon.com/clouddrive/share/bSuTh0sDSjlydgs2IZi9gAehCYHE1TCLjUuDP7YeEXw?ref_=cd_ph_share_link_copy
note that I do not fix the hole polygons, as that is not the problem here, but they need attention! [you can download this]
I would select one side of the curtain, just enough to get a thin model from it, not the “Extruded Version”. Then fix the problems around the holes (I would check if an Alpha map hole would be possible!). Since the mesh intersected before, that reduction first seems a good idea anyway. This can be then easily relaxed. To get a “volume” object back then, this could be done with a single Simulate>Cloth Surface set to a a certain Thickness. UV stays stable then. Cloth allows only one side texturing, not Front and Back [Texture Tag]. To make that possible, one needs to make this editable and go from there.
All the best
Video with some alternative steps. [you can download this]
https://www.amazon.com/clouddrive/share/IsG2NeCv4fBB4yU92nRGpeUCVGqfRzv2Orvr1RBJQvF?ref_=cd_ph_share_link_copy
Again, it contains suggestions and ideas, perhaps not suitable for this object, but perhaps helpful anyway. Of course—I tried to stay focused on you curtain.