I have no doubt that sometimes adults are forced to take a toddler to a place of business. But, to expect that everyone will be understanding and tolerant is a bit much to ask. If you are forced to take a child to an adult setting, I think you are wrong to complain or vent that the other adults weren't tolerant. And sometimes holding a screaming child is safer for the child than letting him run around wherever he wants. Makes it hard for everyone to hold conversations, but the child may be safer.

The guard is responsible for the safety of not just the staff but everyone in the waiting room and in the parking lot. The guard should not be distracted from his official duties by taking care of your grandchild, even if just a few minutes. More work and trouble for you? Absolutely. You said the mother had her own appointment but obviously she didn't take her children to her adult appointment and expect the staff to be tolerant.