The two piece trigger on your 73 is part of the trigger block safety designed into the 73 by Winchester back in the day. It prevents the rifle from firing before the bolt is fully closed. The 1866 has no trigger block safety, and can be fired out of battery - not a good thing.
It sounds like you need to find a good gunsmith who can fine tune your trigger for better function. The fact that it is a two piece is not your problem.