Looking for a set of 2 wireless PS2 controllers which can be swapped around to make either player 1 using only the controller itself

HELLO amazing helpful Lemmitors (Lemmians... Lemurs. Whatever). I hope I can explain this clearly. I desire a pair (2) of PlayStation 2 controllers which work wirelessly via the SAME wireless dongle stuck into BOTH PS2 controller ports at the same time. This allows me to turn one off while my friend on the other side of the room turns theirs on in order to switch who's controlling player 1 for taking turns in single player games without having to throw one controller back and forth across the room. You may laugh but I have managed to find and purchase a controller that does exactly this off eBay, which is a ProGamer (brand) PS2 wireless 2-controller set with a single dongle that splits into 2 wires and plugs into both controller ports simultaneously and does exactly what I described. The problem is one of the controllers has a faulty analog stick that doesn't activate when going left, and I can't find this brand or this type of controller or anything like it to replace this set up. If you have any thoughts or solutions I would much appreciate it. Thank you 💚

And I should note that I'm unconcerned about the quality of the controller since my main requirement is for it to simply function properly and work in the ways I described. Thanks