How do I resolve unsuccessful refunds for accidental app purchases?

This is a user forum. You are not talking to Apple.

Contact apple support.

Click on the link below, you can

• View your purchase history

• Cancel a subscription

• Request a refund

• Verify unfamiliar charges

• Add or remove a payment method

Subscriptions and Billing - Official Apple Support

It may be that you owed Apple money for something else and once it saw you have the funds in your balance it automatically withdrew it.

Avoid accidental purchases

1. If it is your device then, please --> Use Guided Access with iPhone, iPad, and iPod touch - Apple ... before handing over a device to a child.
2. If it is your child's device then in the future, enable the Ask to Buy feature --> Request and make purchases with Ask to Buy - Apple Support

It could be Phishing

• Beware of --> Phishing & Other Suspicious Emails 
• Know how to --> Identify legitimate emails from the App Store or iTunes Store 
• Avoid phishing emails, fake 'virus' alerts, phony support calls, and other scams —> Use these tips to avoid scams and learn what to do if you think your Apple ID has been compromised.