You don't mention any effect of not being told about the penicillin allergy, or that your kids' 2nd doctor had any trouble treating them as a result fo the files taking as long as they did to transfer (especially since the new doctor got the records in June and you didn't take your kids in until October), so it's unclear what your concerns are about that.
You're best off asking for and keeping digital copies of all of your own and your kids' medical records.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
To answer your question, the law is Cal. Health and Safety Code § 123110 (b), which reads as follows:
[A]ny patient or patient's representative shall be entitled to copies of all or any portion of the patient records that he or she has a right to inspect, upon presenting a written request to the health care provider specifying the records to be copied, together with a fee to defray the cost of copying, that shall not exceed twenty-five cents ($0.25) per page or fifty cents ($0.50) per page for records that are copied from microfilm and any additional reasonable clerical costs incurred in making the records available. The health care provider shall ensure that the copies are transmitted within 15 days after receiving the written request. [Emphasis added.]
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