I want to change the administrator ID on my new MacBook Air & MacBook Pro & separate how the 2 laptops communicate

1. Create a separate Administrator account for yourself, assuming you have not already done that: Set up users, guests, and groups on Mac - Apple Support
2. When setting up iCloud, use your Apple ID: Set up iCloud on your Mac - Apple Support. Do not attempt to share a single Apple ID; that is what's causing your difficulties. Use Family Sharing instead.
3. When each of you are satisfied your respective Macs are working the way you need them to work, have your wife log into your new MacBook Air under her Account, and follow Steps 3, 4, and 5 in What to do before you sell, give away, or trade in your Mac - Apple Support. Don't erase the Mac (obviously).
4. Then, have her sign out of her User Account for the last time.
5. Log in to your Account and delete her User Account: Delete a user or group on Mac - Apple Support

Be advised that you won't be able to update any apps or similar digital content she purchased under her Apple ID unless you provide her credentials. Some apps permit Family Sharing, some don't, but as long as you remain familiar with one another asking her to provide her credentials when needed shouldn't be a concern.