First of all, I hope you showed the email to the principal. It sounds as though that mother may be trying to accuse you of discrimination, and that is a serious subject and charge. It's best to get your principal/supervisor/department head in on it right from the start.
I don't know if you're a parent, but in many cases, there is a lot of guilt involved in parenting, especially with a child that struggles. It's much easier on the conscience if a lax parent can blame others for the problems of the child, for the failings of the parent to supervise and discipline their child. Some parents don't have the time, or the skills, or the desire. That's just the way it is.
As long as you're keeping close documentation on the problems with her child, and keeping her informed so she isn't blind-sided when he possibly fails the class, you're doing your job as far as she is concerned. She should have a face to face conference with you, maybe with someone else there for support.
Have you asked other teachers if he is the same way in their classes? Sounds like it's time for a case conference, with the counselor if necessary.
As for your frustration...Bill Cosby said "I don't know the key to success, but the key to failure is trying to please everybody." You do the best you can and realize you are not going to be the end all, be all for every single student. Whatever you do, don't stoop to her level. Put her email away until the next day. Type up response if you want, but don't mail it until you've cooled off and can go back and read it again, or have someone else read it for appropriateness.
Then treat yourself to something special for being the kind of teacher who truly cares about the success of her students. You have a tough job. Thanks for taking it on!!