Both times I brought my wife into BWI to give birth they took her back to a room and had me wait in the reception area. After ~10-15 minutes a nurse came out and got me. During the time they were getting her changed into a gown, etc. they asked her if she was safe at home and if she wanted me to be there, etc.
They did the same thing with my wife before both births. It's no big deal as long as she knows not to mouth off.