Should not happen, if you do it correctly, and if you set the new device as the Preferred Activity Tracker in the Device Settings » Activity Tracking. Do not delete the old device from GC, just "retire" it, if you do not plan to use it anymore.
Once you retire it in your GC account, make a Master Reset of the watch (look up the manual for the exact procedure - it differs from model to model), and then set up a new account for your son. You'll need to create one in your name (though using a different email address), unless he is older than 14 (?) years. For legal reasons, the accounts of youngsters need to be maintained by adults.
