Hello and welcome to the forum! You raise some good questions. As the Primary Account holder only YOU can indeed make any changes to your phones in terms of plans and features. Any kidnapper (God forbid) cannot call verizon and remove the Chaperone feature or any other feature (unless they had your username, password and private account information that verizon would ask to verify it is you). At best all someone like this could do would be to throw the phone away and no one would have much control over that happening.
In terms of "remotely" updating your features on any phone, you can do that via calling - OR - from your computer if you've signed up for "My Verizon" which is free and I totally encourage everyone to do so. Verizon also has another feature that you should inquire about which is called "Usage Controls" it's $4.95 but has a wealth of even more features that are designed to control your phone even further than Chaparone. You can limit the use of your phone in terms of who can contact your child and who your child can contact. You can control the time of day the childs phone can be used as well as a host of other blocking and restricting items. 
