Sounds like Skype is unreliable for you, I haven’t found it so for me. The other thing that you can try is sending a workout via here where the client can see video and then have a weekly chat via facetime to go over moves and Q and A. This is what I also do with clients rather than walk them through an entire workout.
We go over time, tempo, duration, monitor results for the week and a plan for the following week(s) including strength and cardio.
Have you taken a look at this thread? Looks like some of the trainers here are successful with Skype. You might message them and see how they are making it work.
One of the suggestions I liked was communicating via Skype, sending exercise video instructions, but not trying to coach the workout itself “live.” Maybe that could work on the days that Skype is lagging live.