we keep our dogs and gliders separate, as far as no bonding. Our dogs know
to stay away from the gliders, at least while we are home.
We had a glider jump and run across the floor once, the dog got up and left.
I think you should keep the dog out of the room whenever YOU are not in the room, if that is possible. If the dog listens to you, then you could have the dog in the room with glider in cage, as far as glider out of cage with you in the room and dog in room, I wouldn't do it with my dogs.