All the current video chat systems do not offer simultaneous bi-directional audio communication. The programs switch from one person to the other. People can't speak or play at the same time and be heard at the same time in a useful way. That's what was going on in the OP story of a lesson. Don't play at the same time. One play, then the other plays. Send the students the backing tracks to play on their end.
Skype, Facetime, Facebook messenger, Google, WhatApp, Zoom... they all work.
FaceTime (Apple only) to my eye has better visual quality but stalls more often than Skype. Skype is pretty solid.
What I like about Zoom is the ability to schedule lessons, and not receive calls from others during a lesson, also the record function is easy to use, so you can record section summaries for your students and share them later once the lesson is done. Zoom has a 40 minute time limit, so not good for 1 hour lessons. Stopping and restarting is a bit lame for a paid lesson. If you like Zoom and are teaching a lot, looking into the paid version.
Plugging in with your RJ45 ethernet connection is better than using wifi from a reliability, stability and speed standpoint. But if using a tablet or phone, then wifi it is, so try being close to the router and choose the 5GHz network instead of the 2.4GHz.
Also use headphones to hear the students and not speakers! Makes a huge difference.
Here is an article that might help.
How to Teach Online Music Lessons and Earn Money