One twin naps and the other doesn't... this sounds challenging C.. Neither of my kids napped so their second and third years were hard for them. I did one thing that helped:
Go to the library and get stories on CD. Most young children's stories are peaceful. She may fall asleep with the story going (which my kids did sometimes even as non-nappers) or she might not. Either way, on the days she does fall asleep she will catch up on the sleep she is missing.
Some kids are just too busy in their minds to sleep. Giving her mind something to do while she is resting will be regenerating enough for her. A busy mind, with something to do that is not physically active, will feel rested after stories and books.
If you want to spend this time with her yourself, go to the library and pick out chapter books (Winnie the Pooh, Francis, Little Bear). This way YOU are directing her brain activity.
What ever works - do it so that you can get some free time and her brain activity can slow and rest for a while.