Well that's good news and potentially not so great. The good news is it sounds like your calcification is relatively minor, though you're still waiting on your doc's additional analysis. The bad news is that remaining stone is not treatable so you might end up passing it and if it gets lodged somewhere or comes out the wrong way (ie, width-wise), depending on its shape, it could be painful like the first one. But maybe you'll get lucky.
I don't know much about dissolving stones through home remedies. Acidic juices are purported to help with that, but it didn't work for me and it sounds like your doctor's not convinced of the merit of that either. I'll let you know if I see anything that doesn't look like quackery.
I do still have my kidney stone prevention info from when I got them chronically. It was only when I cut out gluten that I got any results, though I think that water probably would have helped if I hadn't been eating "healthy whole grains."
For calcium oxalate stones, some of the other preventatives that were suggested to me or found in the past or recently and make some sense to me are (this is meant to give you possible leads, not to be prescriptive):
> increase dietary magnesium (to help absorb calcium and prevent free calcium accumulation in the body fluids)
> increase dietary calcium but avoid calcium supplements (
http://www.medicinenet.com/script/main/art.asp?articlekey=1887); poorly absorbed calcium can actually contribute to calcium oxalate stone formation, but well-absorbed dietary calcium, such as from mineral water, appears to help
> increase dietary potassium
> drink lots of mineral water (
http://www.mgwater.com/kdneystn.shtml)--since some mineral waters contain magnesium and potassium and some also contain calcium, in apparently highly absorbable form, this helps out with the three above tips as well as hydration
The tips that make less sense to me now include:
> limit vitamin D intake: I found this in my old notes as well as online; it seems counter-intuitive and doesn't seem to have as much support as increasing magnesium and limiting protein. The one study I found involved people taking megadoses of calcium in addition to small doses of vitamin D--I suspect the megadoses of probably poorly absorbed calcium more than the vitamin D (
http://www.vitamindcouncil.org/newsletter/2006-aug.shtml).
> some said to limit fish due to oxalate content, but others disagreed (interestingly, fermenting fish reduces its oxalate content)
> and other obviously bogus advice like eating lots of whole grains
Other recommendations that you are already doing are high zinc intake and limit protein and vitamin C intake (some people have allegedly gotten kidney stones from taking megadoses of vitamin C), and you're avoiding high-oxalate plant foods, of course