Just to give everybody an update, the GA (as well as the redcoat at security) did let us all through. And this was a GA that was strictly enforcing the boarding order (a must for flights to South America).

I did put my BP on top and handed all 4 at the same time but didn't have to say anything. With two small children, it's obvious we're travelling together.

I was surprised that their BPs said Group 4. I seem to remember that last time we flew together, they all said PriorityAAccess (with only mine having the stamp). Oh well, they got the access anyway, so maybe I'm wrong about last time.