A bit of amateur psychology:
Her problem .... which she has turned into your problem, is that she has been promoted above her level of competence (the old Peter Principle). She is incapable of delegation, even to an employed contractor (you) and feels compelled to keep on "top of the task" just to prove who is the paymaster. I have no doubt that she is also given to bitching about "Glass Ceilings" and how she has to "Work twice as hard as men just to prove she is as capable". Clearly she is not as capable and got her position through pulling the old "You won't promote me because I am a woman" routine. She is insecure because, at heart, she recognises her own incompetence and is scared witless that she will be found out. When she is it will be everyones fault but hers.
Personally I should complete the task, cash the cheque and then put a report of the difficulties you have had working for her to a level well above her within her organization explaining why you will not be able to "oblige them " in the future.
The Education and the Health sectors are full of such people.
The latest nonsense to come our way is that Mrs S has now been told she must attend a 30 hour course to learn basic literacy and numeracy skills to an "approved level" in oder to complete her Post Graduate Certificate of education before they will give her a licence to teach.
Given that she has 11 O levels, 8 A levels and an BA Honours Degree with Diploma in European Humantities, has been teaching Latin, English and History for years and is currently employed by Coleg Harlech to teach basic skills to "fragile members of the community" via the medium of Arts and Crafts I feel this is a bloody cheek but the hoop has been designed to be jumped through by a Miss Whiplash equivalent under NuLabour policies to ensure all teachers have a command of the basics. I.E, It is the Government's sop to complaints about non British teachers with a dubious command of the English language that they have been importing whilst qualified teachers have been siphoned off onto false career paths in "education".
My advice to her is the same as to you ... take the money and then stick up two fingers.