Talk to a pool supply store, and ask them for advice. You might not want to say what it is exactly that you are repairing though.
LOL, as I was reading the thread, I was remembering how I repaired several pairs of mine. I've got a broken spring in my truck seat, and if I'm not careful getting into the truck, it pokes through the seat and right into my jeans, and right through my plastic pants. I've accidentally done that about 4 times.
But on to the fix. I had this pool repair kit that I had gotten from Walmart, and I figured "why not?", it's made to work on plastic, {vinyl}, so I tried it, and it worked. The kit came with this thin, clear sheet of patch material, and some glue. I cut out some pieces just big enough to cover the hole on the inside and outside, and glued them down. When I ran out of glue from the kit, I use this stuff I got from a model store, it's called "Plastruct" plastic weld general purpose plastic solvent cement. It's a clear liquid in a glass bottle, and has a brush attached to the lid so you can brush it on. It seems to work great for this, as every pair I've patched is still holding just fine. I've even repaired the side seam on one pair when it came apart about 4 or 5 inches. I've done it with just the glue on the seam, but it works much better if you apply a small strip of the patch material with the glue too.
Hope this answers your questions and helps everyone with this problem.