I cannot transfer my child to my family group; the request shows pending on my device, but my wife is not receiving a request on her device.

Hello DoctorMuch,

Thank you for reaching out in Apple Support Communities. To confirm, were you able to follow the section of this support article that says, "Approve the request"? Move a child to another group using Family Sharing - Apple Support

If so, and this behavior continues to occur, let's ensure that the device your wife is using is updated to the latest version of iPadOS 16.3.1 or iOS 16.3.1. This provides software improvements that may help in this situation. Here's how:

Update your iPhone or iPad wirelessly

1. Back up your device using iCloud or your computer.

2. Plug your device into power and connect to the internet with Wi-Fi.

3. Go to Settings > General, then tap Software Update.

4. If you see more than one software update option available, choose the one that you want to install.

5. Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do.

Following these steps may help and is outlined in this article: Update your iPhone or iPad - Apple Support

If that doesn't help, we recommend to contact Apple Support as they can investigate this further. You can contact them by using this link here: Apple - Get Support

Best regards.