The MAXIMUM dosage for Tylenol is 4000mg in a 24 hour period, which equates out to either 650mg {2 regular strength tabs} every 4 hours, or 1000mg {2 extra strength tabs} every six hours. That is the dosing for an adult, and even at the hospital we do not EVER exceed this dosage.
Also, a child should not be giving the guidelines or parameters for medication administration. My 7th grade child has been on prescription medication for years, and knows exactly what she takes, how much, and when, and even then I would NEVER send her to school with meds to administer to herself. The school faces a HUGE liability if they allow her to do this. Any meds should be brought to the school nurse {or office/teacher if you don't have a school nurse} by the parent {NOT the student}, in the original bottle labeled with the student's name, the med, the dosage, and the administration guidelines, along with WHOLE pills, NOT crushed or split in any way. That bottle should remain at school. Also, there should be a log kept of what she takes and when. The administration guidelines on the bottle should never be deviated from in ANY way without a written note from her doctor's office, faxed in {NOT brought in from the parent} from that office. The written guidelines from the med bottle should trump parents' "authorization" every single time. And along with the instructions should come a detailed description of the condition for which she takes these meds in the first place
Even if you are not governed by the state, you will still have to answer to them if something goes wrong with this child {or someone else's child who got hold of the meds} because of a medication issue. Definitely say something to the administrators, and make sure all your ducks are in a row regarding accountability for administering these medications. Then if the mother calls obsessing about the meds, you can just assure her that they are being dispensed according to the doctor's instructions. I'm with you, it does seem very odd that the whole family would be so preoccupied with medications. I hate to make assumptions, but "Munchausen-by-proxy" was the first thing that popped into my head when I read your description of what's been going on. A visit with the doctor's office when the school gets that note might not be a bad idea.