Back to the chemotherapy argument that Uberiel originally advanced: I don't think there's a more clearcut example available of where to draw the line on a parent's "rights" to control the destiny of their child than this one.
Children should have exactly the same rights as adults under law. In practice though, children, even healthy and informed ones, are often not emotionally or intellectually equipped to make such serious decisions about their own health. This 13 year old is frightened and sick and doesn't want to go through the pain and discomfort of chemo, which is natural, since no one he knows and trusts has apparently clearly explained the alternative to him, and rather than helping the child understand the situation, the parent is actively standing in the way of the child's fundamental right to the treatment he requires to live. If an adult wants to make that determination, weighing all the pros and cons in an informed manner, that's fine, but it's another to force a child to live or die by that kind of decision when the parent is cherry-picking the reasons.