@NoraCuspidora That's strange, that is the one place in the game where the Hold command has always worked correctly for me. Just make sure that after you take control of a character you remember to tell them to hold again before switching to a different character (if you pause, the hold command should show up next to the name of the characters who are currently holding). Other characters should only teleport to you if you get too far away from them.
When I do this puzzle I have one character hold on the floor tile, one next to the main lever, one who runs around to light the torches (and to do the wheel thing in the second cage where I believe the mosaic piece is) and one for the lever in the cage. I haven't played in a while and my memory sucks, but I think that's what I do. Sometimes I forget to retell someone to hold after controlling them, which mucks things up, but I've never had characters teleport in that room. I have never had to use the tactical camera for this puzzle. If it's at all relevant, I use mouse & keyboard, not a controller, I don't know if that makes a difference at all.
If you still have issues, perhaps try turning your graphics settings down. May seem unrelated, but having the graphics settings too high for your computer can cause random weird bugs and glitches, so that could be why your characters aren't behaving properly.
I'm not sure what amulet you're referring to (I just do this puzzle to get through the tunnel into the area beyond, and to collect mosaic bits along the way 😛 ), but there are several mods which change the stock of shops to sell things like accessories, version 1.9 of this mod adds all accessories available in the base game to a shop in Val Royeaux, so the one you're looking for should be in it. If you don't want to use mods, there are no console commands in this game, so you can't cheat an item into your inventory unless you use Cheat Engine, which comes with its own (possibly game/character breaking) risks.
Hope that helps 🙂