I am trying to find a replacement for this connecting part on a ballet barre. It's kind of like a long tee clamp but internal. The poles it connects to are aluminium. Essentially 2 of the key locking mechanisms have jammed so I can't tighten them and I've bent 2 allen keys trying to lock them. Thanks in advance!
As a generic term, those are called "structural pipe fittings" and that is a "Tee". As to the specific brand and type with the internal connections, that's likely something proprietary to that supplier, most likely because it is being used for ballet, so they wouldn't want things protruding that could cause injuries.