How to Safely Lift and Hold a Small Dog | Dog Training Nation
Found this article on the net w/videos as it might be helpful to visualize how you may have wanted the pups to be held.
Suggestion that you could share with the staff that felt that the pups weren't supported well and you felt that they could have been dropped.
I understand your perspective on not seeing the pups while you were checking out but give them the benefit of the doubt here that you had 3 pups (you and your mom) and lots going on that they were just trying to help you out before you got back on the road to get home or your next destination.