What I have found works for me when it's something like that is two things:
1) I would calmly explain to the family that while I understand their concern, I can not call the attending for that. After hours are for things that can not wait till morning. If you have a white board in the room, I would write it on there and say so that it can be a reminder when the attending gets here. I would also say something along the lines of if something comes up that I would have to call the attending, I will let the attending know that you are requesting this. I'm assuming you are night shift, so I would tell the family even if I had permission from the attending to call the specialist they will not be here till the morning anyway.
2) when talking to the attending, first I would ask the important stuff and then latch on oh also FYI, the family is upset the specialist wasn't requested.
I have learned to do that with certain MDs that way they don't think you are the one pushing it. Sometimes when the MD starts getting upset I say hey just doing my job, that's what the family wanted me to tell you so that's what I'm doing.
A lot of not people really back off when you say that. Not just MDs but I've had social workers, dietians, physical therapist back off too.
They still get upset but it's usually not directed at you.