Child buying apps - refund

and Apple have agreed to refund me.

If Apple has approved your request, see this Apple article: Check the status of a refund for apps or content that you bought from Apple

Check the status of a refund for apps or content that you've bought from Apple – Apple Support (UK)

When will I get the money back?                                            

If your refund is approved, the funds will be applied to the same payment method that you used to buy the item. 

Here's how long it takes for a refund to appear on your account or statement:

Store credit – It may take up to 48 hours to see the refund in your Apple Account balance.

Mobile phone billing – It may take up to 60 days for the statement to show the refund. Processing time may be affected by your network provider. You can contact your network provider for an update.

All other payment methods – It may take up to 30 days for the statement to show the refund. If you can't see the refund after 30 days, contact your financial institution.

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My daughter bought two apps from the App Store

To avoid the case in the future, see ⤵️

If other people have access to your iPhone or other Apple device, change the device passcode and never share it with others.

Change your Passcode -> Use a passcode with your iPhone, iPad, or iPod touch - Apple Support

Change your Apple ID password -> Change your Apple ID password - Apple Support

• Create a strong password for your Apple ID, It is best if your password consists of eight or more characters and include upper and lowercase letters, and at least one number. You can also add extra characters and punctuation marks to make your password even stronger. 
• Never provide your password, passcode, security questions, verification codes, recovery key or any other account security details to anyone else. Apple will never ask you for this information.

Then see this Apple article: What to do after you change your Apple ID or password

What to do after you change your Apple ID or password - Apple Support

Require a password for App Store and iTunes purchases

Require a password for App Store and iTunes purchases - Apple Support

Manage App Store purchases, subscriptions, settings, and restrictions on iPhone

Manage App Store purchases, subscriptions, settings, and restrictions on iPhone – Apple Support (UK)

Prevent in-app purchases from the App Store

Prevent in-app purchases from the App Store – Apple Support (UK)

if you still need help, get support from Apple directly -> Get Support or call Apple in your region see -> Contact Apple for support and service or check -> here for more support and assistance.