I got a non-o visa in Chicago by showing them documents from the school and my daughter's birth certificate proving the relationship. Before the 90-day single entry visa expired I went to Samui immigration with proof of funds (bank statement and bank guarantee), documents from school, Google map with gps coordinates of our house and again her birth certificate and we were both issued a one-year extension the same day.
I don't know if you need a new Visa or can extend the one you're already on.