I think I suffer greatly from under-confidence

If you have the time and inclination to test this, you can use this site to discover your level of under- or over-confidence, and adjust appropriately.

In any case, welcome to LessWrong! I look forward especially to hearing about the process of unschooling; there is (very rightly) an impression here on LessWrong that raising a child is one of the hardest tasks; it seems like also taking responsibility for their education is even more daunting!