We have a magnolia in our postage stamp sized front garden. Its getting bigger every year, and last year was the first time I noticed how dark our front room was. In the past its actually provided some privacy and its been great - cos I hate net curtains. So after the last Magnolia bloom, DH 'thinned' it, and it was brilliant.
So, I do understnad when your neighbour complains of it being dark/preventing sun etc. And I do understand your plight about it providing privacy.
I dont think however, there is an argument here to say that 'she knew about the tree when she moved in or bought the house' because she may not have known the consequences at the time. Also, the tree may have grown - trees have a habit of doing that LOL.
I would accommodate her, meet her half way and accept her invitation to use her sons friend, a tree surgeon, and have it thinned and possibly trimmed down a couple of feet. I doubt a couple of feet will make a difference to your privacy (although of course Im not there to see it) - and heck! if we have a summer like last year, rain and sun, it will grow back pretty quick, and you will have won points all round - you have your tree back with a little bit of Gods provision (sun and rain), and she will be satisfied because you have let her trim the tree.
Win win situ me thinks - HTH ?