Chase was a poster a while back who managed to regularly crank out a successful Skype podcast with Audacity. That’s one in a row. Most people get what you got. It gets almost there but is missing a piece.
Neither Audacity nor Skype Play Well With Others. Sometimes they tolerate each other just enough to give you a false sense of confidence, then Skype decides to change a service or setting in the background and your show collapses.
Audacity is not recommended for this job.
Pamela does well. Their licenses can record the sides of the conversation split so you can correct one without messing up the other.
http://www.pamela.biz/en/products/
Other software products are available. If you find something that works, do post back.
https://forum.audacityteam.org/t/help-recording-with-a-mic-laptop-and-headphones/35068/6
You might also look at voicemeeter.
http://vb-audio.pagesperso-orange.fr/Voicemeeter/banana.htm
They can create custom sound channels in your machine and then allow you to control them.
Koz