Ugh. So sorry you are hassling with this, and hope some that have taken it or researched it happen along.
I'll mention some stuff about kidney stones, as I'm too familiar with them as I've had them since long before my DS, and have to stay on top of them like never before.
Nothing can actually dissolve stones once they are formed, but they are finding probiotics show promise at preventing them from forming, and possibly helping break them down. They know that people with oxalobacter formigenes in their gut are 70 percent less likely to develop kidney stones than people whose dietary tracts lack that bacteria. O formigenes is believed to prevent stones by breaking down the calcium oxalate in the intestinal tract before it can ever get to the kidneys. There is no product yet that has O formigenes that we can purchase, but one that is very similar and may have the same benefit we CAN buy is "VSL3" and a prescription version which is much stronger is "VSL3-DS". I take it, and get it through Costco.
Other studies with lactic acid bacteria that included Lactobacillus acidophilus, Lactobacillusbrevis, Streptococcus thermophilus, and Bifidobacteria infantis can reduce urinary oxalate excretion by 24-40%. That almost certainly helps reduce stone formation. Some probiotics that we can purchase with these strains are Accuflora Pro-Biotic-Acidophilus from Northwest Natural and Align Digestive Care from Proctor and Gamble.
Last kidney stone thing, is make sure you don't have low citrate (need 24 hour urine test for that). We often have a combo of high oxalate and low citrate, which is a recipe for making cal/oxalate stones. You can take Uricit-K to address the low oxalate with is a prescription potassium.
I'm not sure if its the urocit-K, probiotics, or both, but I've gone from stones ever 1-2 weeks, to going 2-3 years between, and haven't had a real trouble maker that stuck or got huge in mb 5-6 years.
Since I'm paranoid about bone loss, I asked, and was told, that taking any of these things would not be detrimental as far as bone loss.