A disgraceful series of conduct. If they are so unwilling to let you (honestly) do the work yourself and are presenting with the assumption that self-chosen self-done improvement of something is misconduct (they sound lazy and secretly embarrassed that you are unintentionally showing them up), possibly quietly discovering to them that the coop, that was bigger than promised, is so dangerous and cramped to be actually cruel. As the parents of a minor (I'm assuming) they are legally responsible for answering an inspector from your Ag Department or Humane Society/SPCA, paying the fines, etc. Some jurisdictions keep a list of people guilty of animal cruelty and use it to restrict their employment, that might get them to consider this an actual problem that you are trying to keep them out of.
(People who put their finger on the scale to gratify their empty feelings that and even forbid considering risks because they want to live in ignorant bliss are some of the worst to me. You have my sympathy.)
The advice is just ideas; I can't be specific or any firmer because I don't know you or your parents and I can't take private information from you that would change that. I wish you well and your chickens well.