Having been through this with SD, I know what I will do in the future. SD went in early in the evening and had GD early in the morning. She didn't need us all there all night. Knowing what I know now, I would have made a few appearances, brought food and coffee for those brave (stupid) souls who were there all night, checked in by phone every couple of hours, and made my presence known while getting a half-way decent nights sleep.
So, do stop by and spend a few hours there, and depending on when labor starts and when she is likely to have the child, time it so that you are there as close to the birth as possible. Your DS does need your support in this, so give it to him, but don't do the marathon birth watch thing. That is too much to ask of anyone. Ask him to call when he can, show up with coffee and treats for the marathoners every couple of hours, and be in the waiting room as close to the birth or as soon after as possible so you are there for him to show off his child. He wants and needs you there, so be there, but be reasonable about it.
It is a damned if you do, damned if you don't situation. It was for me and my kids, too. So, do what your conscious dictates. Your DS needs you there, so be there, but be there only as much as you are comfortable. It seems like he needs her family to understand that there are two families here, not just their family.