Originally Posted by
pgoat
The lower busted off hanger fragment looks a bit warped, I'm afraid, with the RD mounting hole portion pulled noticeably inward (as if pulling in towards the wheel's spokes)...so correct me if I am wrong, but that makes it a clear case of needing a new dropout entirely, yes? My guess is even if a welder can join the two halves, aligning the rear end for shifting and a straight chainline would be difficult or impossible
It's possible that the reason the dropout broke is because the derailleur went into the spokes at some point and bent the dropout and started a crack at the adjuster bolt hole. Those cast dropouts were difficult to align even when intact, and when re-welded might not be strong enough to withstand re-alignment.
Here's a possible approach: get the dropout re-welded and check the tab alignment. If it's way off, cut off the hanger tab and use a bolt-on claw,
as was suggested above.