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I am sorry to hear about your dog's condition and I wish her the best for a complete recovery.
Bladder stones can be secondary to infection, and in cases of struvite stones (unless she is a bichon as these dogs will form sterile struvite stones) they re certainly related to the infection in her bladder. The infection will not go away unless the stones are removed as the stones can serve as a nidus for infection and bacteria can hide within the cracks of the stones causing re-infection. In this case, we have no choice but to do surgery with an infection present in order to treat her properly. Dental disease will not cause bladder stones.
In cases of bladder stones, yes it is normal to do surgery on dogs with infection as we have no other way of controlling it without removing stones. Additionally, for some infections, surgery is the only thing we can do for source control. So, to answer your question yes it can be normal to do surgery on a dog with an infection but in reality it all depends on the type of infection, the surgery that is being performed and her general state of health.
If the infection is related to the stones, perhaps they should have performed surgery sooner. Without having the records to examine what they did do and why they did it, I cannot say with certainly that they were right or wrong by waiting.