What should I do if my app refund request is denied from Apple?

I have never heard of Apple telling any user the a refund is guaranteed, so not sure why that would be relayed to you. Any purchase requires the person to double click the side button with the amount showing on the screen followed by verification using biometrics or the Passcode to your device. If your 2 and a half year daughter is capable of performing those actions on your phone, then you need to use additional protections to prevent that from happening, such as requiring a unique password for purchases.

Require a password for purchases in the App Store and other Apple services - Apple Support

In most cases all transactions in the App Store are final and it is only in some cases that a compassionate refund would be granted. It really makes no difference if you use the app or not, the same is true for any subscription such as HBO/Max where you will pay the monthly charge whether you watch any of the shows or not. It should never be expected though. If you do disagree with the final decision you can view the information provided here:

If you disagree with your final decision, contact dpo@apple.com.

https://reportaproblem.apple.com/static/en-us/privacy.html

"I've had similar situations where I made a wrong purchase myself and they refunded my money."

The people responding on this support forum are users like you. We have no special access to Apple information or your accounts, so unfortunately all we can do is guide you to the information Apple does provide. Apple, however, does not have much on its criteria for refusing refunds. Here are two sections from the U.S.A. version of Apple Media Services Terms and Conditions - Legal - Apple Media Services - Apple You can see if the terms are different for where you live by clicking on this link Legal - Apple Media Services - Apple select your location and then your language.

- "All Transactions are final."

I understand this as meaning Apple is starting from a point where any refund is considered an exception. Apple may provide a refund but can also simply say no without having to provide a reason. I understand this can be frustrating but by using the service you agree to the terms.

- "From time to time, Apple may suspend or cancel payment or refuse a refund request if we find evidence of fraud, abuse, or unlawful or other manipulative behavior that entitles Apple to a corresponding counterclaim." It may be certain refund requests might be considered suspicious or—given what you said about previous refunds— excessive. Again, technically they are not under any obligation to make any refunds.

MaarCarrillo wrote:

But even so, I don't think it's fair that my refund was rejected when I've had similar situations where I made a wrong purchase myself and they refunded my money.

Anecdotal evidence indicates that if you have been given a refund in the past for "making the wrong purchase," you are less likely to get a refund in the future. It appears that Apple gives you a "freebie" the first time you ask for a refund for such a mistake, but after that, you need a reason, such as the app being fraudulent in some way.

Please use the link I provided on the bottom of my previous post. I do not question your sincerity and understand that it is very frustrating.