How to add group video chat to appointment

I'm setting up a site where a personal trainer can set appointments with the Appointment+ plugin, and then for the appointment they would use a group video chat (Hangout, Skype, other?) for the appointment. Out of the box this can be accomplished by manually using something like skype and "calling" the user that has the appointment, but I'd like to make it cleaner. Any suggestions would be helpful. Thanks.