Hypos are dangerous, and so are doctors who will not listen - I'd be asking him if he is available to come to treat the hypos he is causing by insisting on what seems to be an overdose - maybe send him the readings you are getting with a note to the effect that he might possibly be wrong.
I don't take insulin, but it really is a bit obvious what is happening to your sister.
She could be producing some insulin, which is why she doesn't need the amount calculated.