Apology Letter For Questioning Your Judgement
Dear {Recipient},
Please accept my humble apologies for questioning your judgment on {subject}. I thought you were making a mistake when you decided to {action taken}, but clearly I was the one who was mistaken. Your {knowledge/expertise} about the {issue/topic/situation} enabled you to make a very sound decision for the benefit of everyone involved. I'm sorry I doubted you.
Sincerely,
{Your Name}