J.F.
Depends on your area, and cost of living. How far is she going to drive each way? Is she coming to you, or are you driving your son to her? Meeting at a library (be careful with that....libraries usually do not allow people to charge others while using their building). Is your son easy to work with? Easy to distract?
I tutored privately in MN. I charged $40 an hour. I have my degree in education, taught in the classroom for several years, and ran a franchised tutoring business for 2 years. I drove to the student's homes, and tutored for an hour for each session. I also emailed, and met with the students' teachers.
I think $30 for the hour's worth of work is on par, but I don't know your area.
Also, ask her what she charges. If less than $30 a week, offer more than what she is charging, and you will be sure to have a consistent, and happy tutor on your hands. If she leaves it up to you, put it back in her court. She needs to learn to advocate for herself. You'd be teaching her the lesson. :)