They get to the hospital with plenty of time to spare. Elsa's ushered into the birthing suite to wait for an anaesthetist. There'll be some doctors on hand too, just in case she needs to go in for surgery. She's told to walk around the small room, or make use of the exercise ball.
They never did go to those birthing classes.
Anna doesn't even have time to feel useless because every contraction sends Elsa moving towards her, holding her arms out and seeking a familiar comfort.
She doesn't feel useless because... Elsa needs her.