Hello @mcatselfprep,
hope you’re doing good today! ??
First of all, you should select the A+ <-> GCal option, so any changes happened in each end, will inform the other (complete synchronization).

I already tested that in my end, and after removing the appointment from both backend as an admin and from frontend using the [app_my_appointments allow_cancel="1"]
, resulted in the GCal event to be removed.
If you already use the above option, then this should be happening due to some conflict with another plugin/theme, so please the followings:
– backup your website (files & database)
– deactivate all plugins apart from Appointments
– activate a default theme like TwentySeventeen
– try to add, then remove/cancel an appointment and check GCal
If the issue is resolved, start activating the remaining plugins and theme, one by one this time, making a little add/cancel test each time, until you replicate the issue again, thus finding the conflicted combination.
Let us know, how that goes!
Warm regards,
Dimitris