I understand your anxiousness over this, it's completely normal.
As far as I know for visits such as this you would most likely be in the examination room with your gliders. Surgeries and perhaps some other procedures would be different, but for well visits and most likely nail trims you most likely will be in the exam room.
The Dr. and those in the room are trained to work with animals. If they are experienced with gliders than they should know what to expect behavior wise. Your glider's behavior is unpredictable until you see how they actually do in this situation. Besides that, each glider has different personalities and so one may do better than the other.
They will get over it, even if they are upset and may respond differently for a bit, they are fairly resilient creatures and will be okay afterwards.