In the Appointment Reminder template there are three phone replacement tags: $WORKPHONE$, $HOMEPHONE$, and $MOBILEPHONE$. Are these phone numbers of the coach or of the client?

These are replacement tags refer to the client's phone numbers, as they are entered in CONTACTS > CLIENT NAME > “Edit Info” > “Contact Information” section.

The phone number of the coach in an appointment notification or reminder is the Session Phone (with the replacement tag $APPOINTMENT_SESSION_PHONE$). This session phone number is entered by the coach in Communicate> Settings > field “Phone Number for Appointment Reminders”.