If I were Kiddo, I'd use one of the other schools/scholarships for my "boarding school" and then transfer to the school of choice the next year, that much further ahead instead of being a year behind?

My father went to a gap school (in 1930 :-) and one of my brothers did also (very early 1960s); my father wanted to get into the Naval Academy and thought he needed a better background and my brother did poorly in high school through not applying himself and my parents sent him in hopes of giving him a better chance at college, etc.

If you can afford it or work it out, I would do whatever he'd like. However, if it is going to make you uncomfortable and indebted, I would explain that you just cannot do it at this time. He is not his half sibling and circumstances have changed (with his half-sib's situation, that used your "credit" with the relatives and money, etc. and this would be "more" and you don't want to do more). He wants "extra" that isn't strictly needed where as the half had to go to high school somewhere and happened to choose/need the boarding school at that time in half's life.