Peace is a wonderful thing. You can be in labor and be having a really hard time but still be at peace. You could also be relaxed and calm but still not be at peace.
Let's look at the difference.
Peace in it's true form is coming from the Lord. Peace does not come from birth circumstances or from having the right birth team around you, although those two things can aid in your working towards peace. To feel peace and to know peace in a time of struggle you must be able to 100% put your faith in Christ that He will see you through. Accepting what you are going through and knowing that it is ok. Keeping your thoughts fixed on the Lord will help keep your mind away from distracting thoughts of fear. Fear is the number one enemy of birth. When you let fear in, peace goes out the window and in comes tension and more pain.
On the flip side of this, you could be relaxed and calm but still not have peace. Why? Because there are ways to achieve calmness and steadiness without the help of the Lord. But know that they are more temporary than any amount of peace you can receive from God.
It takes great strength during birth to decide that you would rather feel peace than fear of the unknown. And I know you can do this. When you are in labor, keep Christ as your first fixation. That way you have peace and also you have the ability to ask the Lord to guide your decision making. If you are allowing the Lord into your decision making then you are casting out fear and any other plot from the enemy.