What is another suitable and effective word to describe someones 'strength' such as in the following sentence."The story of Elliot's birth focuses on Emily's strength when she was giving birth."
It would be helpful to know the conditions under which Emily gave birth to Elliot. That knowledge might help in finding appropriate synonyms for the word "strength" in that particular situation.
It may be that an acceptable substitute would be "endurance." If the birth was very difficult and took a long time, endurance is certainly an important part of the labor process. "Determination" could also be applicable under those circumstances.
If Emily coped with the stress of labor by focussing on the miracle of what was happening, perhaps "faith" would be an appropriate descriptor. On the other hand, if Elliot was conceived under less than wonderful circumstances, it may be that "anger" or "fury" would be the correct word. If the birth came faster than expected but Emily was still able to give directions and make plans for how to handle the delivery in an unusual location, "calmness" or "control" might be appropriate.