Good afternoon di35,
Welcome to the Apple Support Communities!
It sounds like you and your wife are having issues with the Apple ID accounts on your two iPad devices, and AirPods connecting to the wrong device.
Can you provide a little more information about this situation?
Please reply to this thread with the answers to the preliminary questions below so that we can determine the best course of action for you.
Don't make any changes to your Apple ID, iCloud or device settings until you hear back from us, or unless you contact Apple Support for help with this.
As a general troubleshooting path, we would want to make sure your Apple ID accounts are unique and separate.
Then make a backup of your devices, and enable iCloud to quickly sync and populate important data.
Finally, it sounds like you may need to restore the older iPad to factory settings, and then set it up again with the correct Apple ID and data.
What do you mean when you say your wife's iPad "defaults to your Apple ID"?
Your profile shows an iPad 2 with iOS 9 running on one of the devices. Who uses this iPad?
What is the second iPad model and what iOS is running on it?
Do you and your wife each have a unique Apple ID?
Do each of you see this unique Apple ID in both the iCloud Settings and the App Store / iTunes Store settings?
(It sounds like an email address or phone number is being shared between your Apple ID accounts.)
Manage and use your Apple ID
Manage Apple ID and iCloud settings on iPhone - iPhone User Guide
Do you and your wife have iCloud enabled for your contacts, calendars, photos, etc. for your unique Apple ID?
Turn iCloud features on or off - iCloud User Guide
Your wife should be able to unpair the AirPods from her iPad and choose "Forget this device" in the Bluetooth settings.
Connect and use your AirPods and AirPods Pro
Please provide the additional information requested about your issue and we'll do our best to help!
Take care.