Hello Sarah and welcome to Gransnet. I was birth partner for all 3 of my daughters which makes 6 times now. DD3 needed me both times having been abandoned by both the fathers of her sons and she was my first experience. It is something quite like any other.
Firstly, if your DD's partner is going to be there it might be a good idea to discuss how much input he would like you to have. It is important for you not to get in the way of his involvement. First time labours can be very long and slow, so being able to allow each other time out while ensuring your DD is still supported is useful. And do make sure you take some rest yourself. The last hour or 2 when DD goes through transition (when most mums feel at their worst) and the second stage is when you will need to support her most, so reserve your energy until then.
Re seeing your DD in pain, yes it is difficult but keep thinking of it as positive. I found that my mother's instinct to soothe and help in any way DD needed kicked in. I think you will find that the focus of your concern will be on how she feels, not on yourself.
As other posters have said, go with the flow. Every one of my DD's labours and births have been different.
Finally, be guided by the midwives who know what the are doing. If things are beginning to go pear shaped, which hopefully they don't, they will need you to back off quickly and keep calm.
And don't worry about crying. Most people do cry when the baby is born, partly from relief and partly because it is such a miracle to see a new baby arrive. I cried every time! Good luck and enjoy being a grandparent. Being at the birth is such a bonding experience. The baby will be very special to you.