Hi @Daniel Šimáně
Welcome to our forum!
Please kindly understand that the Outlook tag here we mainly focus on general issues about Outlook desktop client.
Can other Gmail accounts be added to the Outlook client normally?
Based on my search, I'm afraid there is no official document that provides steps to add a child's Gmail account. The work or school account you use with Gmail can be added to the Outlook client as described in this document: Add an email account to Outlook for Windows.
In addition, considering that this issue may be related to the account, and I have found many users in the Gmail community who have the same problem, it is recommended that you contact your email provider: https://support.google.com/mail/thread/13783930/collecting-gmail-using-the-outlook-app-for-child-account-in-windows-10?hl=en.
(Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.)
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