In the front end booking form, when parents select a teacher, the availability of this teacher will show up. So in order to check multiple teachers’ availability, you need select one each time from the staff member drop down list. And parents can only make appointment with one teacher each time. And the best way is asking parents to remember the time booked for the first kid and make sure not to clash when making the second appointment.
Regarding printing the appointment list, you can sync all your appointments to a third party calender, for instance, iCloud calendar, google clendar or outlook, and print all appointments there.