Hello@JoanC2 

1.  The camera has bound to your TP-Link ID, and could not be bound to a different TP-Link ID any more

But admin TP-Link account could be used on multiple phones, so you could log in on your family's phone using the same email address and password used in your phone. 

2. For ' Network unstable' error when share device, please check out suggestions here: 

• Please confirm smart device firmware and Tapo APP are both up to date. 
• You could try a different network, like LTE mobile data on the phone or a different network
• Connect phone to home Wi-Fi and see if that make any difference 

If the same concern, may I know how many families account you've share so far? Tapo camera could be shared to 2 different accounts at most as FAQ here:

How to share your Tapo smart devices (smart plug, smart camera, smart bulb) with your families

If the same issue, can you share the Mac address of camera to us ,the email address to-be shared via private message, please let us know the model of phone and its OS version, APP version, if possible,  thank you