Is what I did considered a violation of Sharia, given that I agreed to have my daughter's broken glasses replaced for free, despite offering to pay for them, after the nurse informed me that the frame was guaranteed for three months?

If the company's policy does not provide for a free replacement of a broken frame due to misuse or breakage by the buyer, but only replaces it if it is due to a defect or flaw in it, then the questioner is not entitled to benefit from this replacement if his daughter was the one who broke it. Consequently, if the nurse violated the company's policy and requested the frame to be replaced as if it had a defect, without mentioning the actual incident, then her action cannot be relied upon to benefit from the free replacement.