Cannot update apps on ipad after changing Apple ID to my child's Apple ID.

Installed Apps are digitally signed and associated with the AppleID with which they were purchased. As such, given that the iPad was not properly prepared for “transfer” to a new user, you will now encounter a mismatch of digital signatures regardless of Family Sharing.

There are possibly three ways resolve your current issue…

1) Start again, properly preparing the iPad for its new owner. This will entirely erase the iPad, removing both the Activation Lock and all links to your own AppleID:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

After preparing the iPad, the new user can set-up the iPad “as new”, with their own AppleID - installing Apps that have been made available via Family Sharing.

2) Assuming the iPad is currently signed-in to iCloud with the new users AppleID, ensure that your have a current iCloud backup - then reset the iPad and restore the iCloud backup. While App-data is included in the backup, Apps themselves are not included in the actual backup. When the backup is restored, Apps that are both available (including those available through Family Sharing) and compatible with the iPad will be automatically reinstalled from the App Store.

To reset the iPad:

Settings > Transfer or Reset iPad > Erase All Content & Settings

After reset, the iPad is set-up from the initial “hello” page with the new users AppleID - restoring from the iCloud backup when prompted.

3) Instead of deleting Apps (which will also delete all associated App Data), offload the Apps (preserving associated data), then reinstall the Apps from the App Store.

https://9to5mac.com/2020/01/21/how-to-offload-apps-in-ios-to-save-space-without-deleting-their-data/

This mechanism exists to prevent unauthorised (read - unlicensed) use of software. All software is cryptographically protected by digital signatures.

Unlike days of old where software could be freely shared between users, using the same installation media, this is no longer possible. PKI signatures are designed to inhibit unauthorised use of software.

While fully understanding what you have done - and perhaps why - perhaps consider that your actions are technically indistinguishable from an attempt to circumvent software licence restrictions. Providing that software titles (i.e., Apps) are installed and used within terms of licence, they will install and update without issue.

Apple will not relax their App licensing controls - as this is a revenue protection mechanism designed to protect software licensing for all Developers - both Apple and third-party who market their products through the Apple App Store.

No debate at all.

You have encountered a fundamental element of how all Apps distributed via the Apple App Store are digitally signed - this signature being locked to the AppleID with which the App is “purchased”.

An App that has been shared via Family Sharing is available for download by members of the Family Sharing Group. When a family member installs an App from the App Store, including those that have been shared, the App is digitally “signed” and associated with their own AppleID account.

As such, the App that you download and install on your devices will have a different signature to those downloaded by each member of the Family Sharing Group. Although the App itself is the same, the digital signatures that confer entitlement to download and update the App will differ between users.

So, in practical terms, the Apps originally downloaded by you to the iPad have a different signature to that of the subsequent user’s AppleID. It is for this reason that you have encountered a problem.