airtag doesn't update location unless it's near my iphone

The Apple AirTag does not actually send location information. Your iPhone "sees" it when it is in Bluetooth range of the tag (~30-40') by Bluetooth.

When another iPhone, not the one that initially paired with it, is within Bluetooth range, that phone also needs to be properly configured AND have an active Internet connection to relay the tag's ID information plus that phone's GPS location (anonymously)to the Apple servers. That is where you would "see" it with the Find My app on your phone.

The following features must be enabled on that "other" iPhone to be able to relay the information:

• Find My: Settings > Apple ID > Find My > Find My iPhone > Find My iPhone (enabled)
• Find My Network: Settings > Apple ID > Find My iPhone > Find My network (enabled)
• Location Services: Settings > Privacy & Security > Location Services > Location Services (enabled)
• Bluetooth: Settings > Bluetooth > Bluetooth (enabled)

I suggest to verify that their phones are configured as such, and try your "experiment" again.

Not sure I have a "good" answer for you. Based on my experience, what Apple says, and what others have reported, AirTags make for poor tracking devices. They are primarily designed to help you locate a missing item, like your car keys.

If your goal is to track your dog, you may want to consider getting a dedicated tracker that is based on GPS, not Bluetooth. Just wanted to set your expectations for this device. It doesn't help, that there's a whole industry out there selling AirTag pet collars, leading people to believe this is what they are meant for ... only to find that their pet removes the collar, or worse, consumes the tag itself.