An early congratulations! When we had our twins (C-section) I was overwhelmed by the number of people in the room. Counting everyone, including two assisting students we had 14 people working in the delivery room! Sit with and comfort your wife until delivery, then stay with the twins until you are re-united. I'm sure she'll agree you should be watching then.
For her a little needle-work and some rest is required before you'll join her as a family.
Best wishes for you all