Could a large kidney stone break a girl's hymen?

No: Exit is distal to hymen. It wouldn't.

Kidney stone: Stones pass down the ureter from the kidney and into the bladder. From there the stone passes out of the body through the urethra. The vagina or hymen is in no way involved in this process.

The Urinary tract is separate from the female Genital tract, even though they are in close proximity to each other. This proximity probably gave rise to your doubt. However, this stone shouldn't have anything to do with the hymen. Consult with your Physician to evaluate if it is truly a calculus (stone) that is the cause of the girl' symptoms or if it is in fact something else completely different

No. The urinary opening is separate and above the vaginal area so it will not be affected