Welcome to the forum!
Yeah, this is a frustrating situation to handle with Inkscape. I've heard requests for a tool (some call it a razor) where you can just drag it across a path and cut it. But that doesn't exist at present. Unfortunately, it's just the way the path operations work, that the one on top is sacrificed.
Other people may have other ways to handle this, but what I do is duplicate both pieces. Let's say A1 and B1 are the originals, and A2 and B2 are the duplicates.
1 -- Put B1 on top of A1 and do the path operation
2 -- Put A2 on top of B2 and do the operation again
Now both pieces are ready to be patched together, by joining the nodes.
Or another idea might be to temporarily close the open path. Then you could use Union. Then after unioning you'd have to edit the part of the path which was open before.
But I'm trying to understand about
....trying to drop in odd connectors....
I can't quite imagine the situation. Do you mean that you would have 2 pieces which are not adjacent, but you want to connect them together? Doesn't that mean you have to actually edit at least 3 pieces - the 2 to be connected, and at least one piece which is getting split in two? I wonder if you could use a closed path for that?
Because if I'm not mistaken, you can Union more than one object. You'd have to duplicate the closed path which would be used as the connector, so that you can difference it from the 3rd piece.
It sounds like a fun project!
