Oh man, that's a proper head-scratcher, isn't it? It's like the keyboard and the iPad are having a little feud and just refusing to talk to each other! But hey, tech can be finicky sometimes.
Okay, let's roll up our sleeves and tackle this. Since you've already tried the basics like updates and restarts, let's move on to some other potential fixes.
1. **Forget the Device**: Head over to Bluetooth settings on your iPad, find the Apple keyboard, and forget the device. Then try pairing it again.
2. **Reset Network Settings**: Sometimes this works like a charm. Go to Settings -> General -> Reset -> Reset Network Settings. But remember, this will reset Wi-Fi networks and passwords, cellular settings, and VPN and APN settings you've used before.
3. **Different User Account**: Try signing in with a different Apple ID to see if the issue persists. If it works fine with another Apple ID, we're getting into some deep-rooted software territory.
4. **Check for Physical Damage**: I'm sure you've probably done this, but double-check that there's nothing visibly wrong with the keyboard or the connector on the iPad.
5. **Battery Levels**: Make sure both devices are sufficiently charged. Sometimes low battery can make devices act all kinds of weird.
6. **Update Keyboard Firmware**: Okay, this is a long shot, but some keyboards do have firmware that can be updated. It’s less common for Apple, but worth looking into.
7. **Apple Support**: If all else fails, it's time to get the experts involved. Reach out to Apple support or visit an Apple Store if possible.
In my honest opinion, if other devices are working fine with that Apple keyboard and your daughter's iPad is also behaving well with other keyboards, it's likely some weird software bug specific to that pairing. Let's hope it's not something more ominous.
Good luck!