I've had 5 stones over the years, and still dive all the time. I'm not sure how many you've had, but even after the first one, you should be able to track the symptoms. I won't dive if there's even the slightest chance one is passing, and you can always thumb the dive on the extremely rare chance one would start the trek while you're on a dive.
The closest I came to having a stone impact a dive was on a trip to Jamaica in 2000. The symptoms came on rather mild the day before we left, and I decided to wait till we returned to the states to seek medical help. Keeping pain pills around can help if you have a delay in getting to a hospital, and I wouldn't recommend diving if you're taking them. Then again, you can never tell how each stone will impact you. The first stone I had took an ambulance crew and the max dose of morphine they could give me for the ride, and it didn't do a damn thing to stop the pain. The rest have all come in a different manner, so it's a crap shoot.
Every doctor I've seen has given me different information on how to prevent them. Diet is usually the biggest one they give you, but it's odd how each stone I've had has the same composition as the next, yet none of them can agree on the diet changes from stone to stone. I've gone from eating everything, to cutting out soda, chocolate, nuts, and tea, to cutting back on meat / protein / calcium (this was a tough one for me), and even though I stayed on these diets for years, they never prevented another stone. The only constant that seems to help the most is always staying hydrated, and I drink a lot of water these days. It made the last two stones a walk in the park compared to the first 3, and I'm going on 2 to 3 years since the last one (knock on wood).
As for how pressure would impact the kidney / stone, I've never even thought about it.
~ Jason