Its really gonna depend on your PM and your area. Around here, they don't give a shit, have had pm say to people just bring them with you.
My daughter is also a postal worker, PSE in a small office, but gets called a lot to work in the late after noon for dispatch at the hub office, they don't care if she doesn't have a sitter, always threatening her job. I watch little man in the evenings when she has to work, but lately, I don't get back until after her start time. Luckily grandpa can usually come home if I can't make.
I have noticed lately, that the hub who never actually schedules her, that would be too easy, they just call and say we need you here now, but last couple days, they have seriously called within minutes of my scanner be docked in my RMPO. I know they can see it because if it fails to download or someshit, they call and tell me I forgot to dock my scanner. Love it when its the sub and I can tell them to piss off, LOL.
It really is just something you have to discuss with your PM or immediate supervisor, they may be ok with it, but around here we are so short in all areas, it would be a problem.