How can I separate or detach two sections/nodes.

The red line is a linked offset of the black line. So to get the nodes to appear on it, I must select Offset > Stroke to path. Now I have the nodes on the red line, but would like to edit this one part by separating them here (so I can move the two sections apart).



I have tried highlighting both nodes and then at the top selecting "break path at selected nodes", but they don't separate. I can combine the nodes on top of each other but am hoping there is then some way to delete it so I can separate the left and right sections.



Thank you in advance.

As far as I know, a path is a single (could be closed) line, but you cannot have additional interconnect between non-endnodes. So that's why joining these nodes will not work. And you cannot separate them (directly) because they are not connected directly.

One way to separate your object into a left and right part would be the following:
1. duplicate the red path you want to separate
2. with node tool (F2) select all nodes on the right part without the two connecting nodes.
3. delete the selected nodes (the left part will remain with a "strange" shape between these nodes)
4. now select these two nodes
5. Node tool: Delete segment between two non-endpoints
6. Node tool: join selected endnodes with segment
Now you will have the left part with a straight connection between these two nodes.

Do the same thing on the duplicate of the original object for the other part.
Maybe there are even smarter and simpler solutions.

well, even simpler...
1. draw a line connecting the two nodes...
2. then mark additionally your red object and Menu | Path Division

Thank you once again Theo! You are truly an Inkscape genius!

I drew a line across the section I wanted divided. I then selected both the line and the red object and went Path > Stroke to Path. And then (with them both still selected), I went Path > Difference. And this eliminated the line leaving a blank space.

Thank you sir!