How are you feeling, now? (edit: Sorry, I was creating my post while you were posting immediately above. Glad you're feeling better.) The women I know who have both gone through childbirth and had kidney stones say the latter is more painful. I've had it, myself, a couple times. The first time was as you described. Kind of a gnawing pain in the mid- to lower back. Slightly off to the side. Some discomfort in the testicle, like I had accidentally bumped one of the boys.
Thump here:
You don't even have to put the palm on the back--just have your wife gently thump with a fist over the kidney area (called the costovertebral angle). Does it make the pain worse?
If the pain gets really bad, you'll know. The pain may travel down lower along the back and to the groin as the stone scrapes its way down the ureter. Or it can get stuck, backing things (urine) up. That part is a real problem. On top of the pain. Very typically when the pain is really bad, people are writhing in pain. It's hard to stay still. (As opposed to appendicitis, for example, where stereotypically people are very very still--they don't want anyone to even shake or bump the gurney.)
Stay hydrated. Usually good advice in general, but if you've got a kidney stone (and don't have something else like CHF in which you're watching fluid intake levels) perhaps you can flush the stone down the ureter. It's OK to take pain meds. That's what the ER is for: morphine.