It sounds like all your issues are related to settings in her phone as well as your own airtag settings. If her phone is always showing up as home regardless of her location, I'm guessing she has the "find my" network disabled on the phone. This would also stop it from relaying the airtag signal.I’ve had four AirTags for about a month now. All I get are notifications that they are left behind. My wife has an iPhone yet it does not give her location and it says it still at home when she’s at work. She has an iPhone and the AirTag is paired with my Apple ID so why isn’t it using her iPhone to give location? In Apple community there’s a lot of discussion about AirTags not updating locations and pretty much worthless so far in my experience. It ought to give their AirTags location instantly since she hasn’t iPhone 11 Pro Max with unlimited data. Disappointed, Seth
As far as the left behind notifications, you can adjust those, add trusted locations, or turn them off in the find my app as well.