I understand the homeschool philosophy and am very happy to teach home educated students.
If you want to gain qualifications I teach students using the ABRSM (Associated Board of the Royal Schools of Music) and they have exam centres world-wide. If you don't have access to theory or aural training lessons there is good training software available and also online sites which, although not as good as a one on one session with a tutor, will help towards those aspects needed for the ABRSM exams. Links available on the resources page.
For children, regularity of lessons is best. Because of the demands on children today with lots of school work and extra curricular studies I usually recommend a half hour lesson once a fortnight for children of junior school age (up to age 10), and a one hour lesson once a fortnight for children of senior school age (11+).
The time slot does not need to be the same each fortnight but can be arranged after each lesson.
If a homeschool child of junior school age wants to have hourly lessons I am happy to do so as long as they are benefitting from them and the hour length is not too long a time for them.
It is always best to start with a half hour lesson and if moving up to an hour seems appropriate it can then be discussed.