Schools admit more students than they can take because they know some will decide not to attend. You don’t actually owe them any explanation, just as they don’t owe you an explanation when they decide not to admit your child. I highly doubt that an AO would take things so personally that they’d not admit a sibling a year or more later. Give them some credit for professional decorum.
My son will write letters to the schools he declines that focus on what an honor it was to be accepted, the difficult things about the school that a hard to say no to, etc. There’s no need to get into what you didn’t like or where you are going. If asked, you can be polite. It’s just not that deep.
And the letter should 1000% come from the student, not the parents!