While I personally did not have kidney stones during any of my pregnancies, my youngest sister did. She had some pretty bad ones, too. I called her to ask what to suggest for you, and she was quite helpful, and VERY empathetic.
Her advice to you is: Push clear fluids, push clear fluids, push clear fluids, and to continue to push clear fluids until they are completely passed. After they have passed, you want to continue to drink lots of water and other clear fluids to keep your body flushed, and to keep the stones from returning. Examples of clear liquids include: water (this one is obvious), crystal light drink, Special K protein water, soup broths (not creamy - and make sure they are LOW sodium).
Also, you want to do whatever you can to eliminate caffeine. If you are drinking a lot of caffeine drinks (coffee, tea, sodas, etc.), you will want to gradually drink less and less so that you don't get headaches.
The build up of calcium in your body can cause these painful stones, especially during pregnancy. If this causes an infection during your pregnancy, it can cause harm to the baby, because of the bladder being so close to the uterus.
Definitely take the advice of your specialist, because they deal with this every day.
Good luck to you,