Jane - we are just back from a week with our son, DIL and our two grandchildren in the States. When grand-daughter was born 6 years ago I was still working and flew over the day of birth with our younger son - he offered to come to carry my bag! - as we drove to Heathrow we got the call to say she had been safely born, had an upgrade on BA and I was so excited I said to the stewardess 'please thank the Captain, its made the day more wonderful' - and she came back a few minutes later with a bottle of Champagne which we later shared with my son. I was able to meet the new baby when she was only a few hours old and saw her then for a couple of days, and together with younger son we held it all together for my son at home.
DILs parents only live a few miles away, so I had imagined that MIL would be of some useful help but it didn't seem to work out like that. So when next baby was due three years later I thought a lot about it and then e mailed my son and asked if I could go over to be the housekeeper/nanny for a while after the birth, but didn't want to step on toes etc etc so he and DIL could think about it. About two minutes after sending the e mail, phone rang, and it was him - DIL had been asking if he thought they could ask me to go apparently, and would I stay for a few weeks.... So three years ago I went a couple of days before scheduled birth date, got sorted with car, school run etc, and stayed for about three or four weeks. Caesarian birth again so I felt I was useful, lifting, cooking, washing, driving - my DIL still laughs and says she never drank as many cups of tea. It was a wonderful time - I made a big point of 'going to my room' quite a bit to give them space - used to spend later evenings on my laptop and had to have an extra case to bring home all the things I ordered online. Her mother used to come and visit - turn on the TV, get waited on hand and foot, watch the laundry going in and out etc etc, and didn't seem at all put out that I was there.
If she has asked you to be there, then go asap - and you can always offer to 'stay down the road' - a friend of mine did that with her son and dil in NZ and that worked for them.