Help Needed: How to Get a Refund from Apple for Unauthorized In-Game Purchase by a Minor?

I'm dealing with a tricky situation where my cousin, who is underage, accessed my iCloud account and made a large purchase of in-game currency while playing an MMORPG without my consent. I've secured my account and I want to know the best way to approach Apple for a refund.

I've taken steps to prove my honesty, like requesting the game developer to delete the purchased items as I haven't used them, because I'm currently facing financial difficulties. As I prepare to submit my appeal to Apple, I'm hoping for some advice on the best courses of action:

- Should I provide Apple with screenshots of my message to the game developer?
- What option should I choose when submitting my request: "A minor bought this" or "I didn't mean to buy this"?
- Is there any specific language I should use to make my case believable to a support agent?

I'm really in need of this money and would even accept a partial refund if possible. Any tips are greatly appreciated!