Assuming that the cadence has anything to do with her back hurting could be a
real bad assumption.
I'm not a doc, but I think the mods you need to make are in your wife's core muscles. This is especially true if she has only recently started riding these distances. If her core muscles are strong, the back problems should go away.
Can you get her to do some planks (no crunches or situps)?
Also, this is incredible, I've done these exercises every day for two years (takes less than a minute), and I haven't had any back problems since I started.
Book.