My old boy Melon had ca. 100 stones removed from his bladder shortly after we adopted him. When we first met him, the poor guy was urinating blood and could not walk for the pain - this must have been building up for quite some time.
Melon's stones were removed and analyzed - his were struvite, the more common sort.
He was put on an Rx diet, Royal Canin Urinary Dog - and remained on this diet for the rest of his life. This was not the 'dissolving' diet, rather the prevention and maintance diet.
We had to be very strict in the first year or so - absolutely nothing other than this food. He ate the dry food, and for treats I would bake the canned food into biscuits. (Only do this on a day when you can open windows - the stuff stinks to high heaven.)
As time went on we could sneak a few extras - he loved yogurt, which as an acidic food was OK for him. A little bit of white fish was OK too. However, we first got the vet to OK anything we gave him. I was overly cautious, as Melon was already an older dog when we adopted him - a second surgery in his senior years would have been difficult.
Struvite stones are most often formed when there is an infection (with the exception of certain breeds where there is a genetic metabolic issue), so we regularly monitored him, doing periodic urine cultures (along with regular blood tests and bladder ultrasounds - he had aother health issues, so this was being done anyway) with an eye to catching any new stone formulation early.
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Do you still have the stones that were removed the first time? They could still be analysed if that wasn't done before.
(How sad am I? All these years later, I still have a little box with Melon's stones and a tooth, right next to his urn... )
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The key thing, IMO, is a good relationship with your vet. Make sure you are comfortable with your vet, choose someone who is happy to take the time to discuss your research and questions, who views the owner as a partner in treatment - and then follow his/her advice.
All the best to you and your doglet.