This is a call-back feature of asterisk. However, I am not able to call your parameter such that you know who is calling and then you make a call to your parent.
For simplicity, whenever I receive calls from your parents with proper caller IDs, your extension will be calls. Whenever you are at home, you may talk for a while and call them using whatever means that you want.
For the ederly, the most convenient to call other relatives who live in other countries like you is to call a local access (telephone) number to reach you. If you are at home, you can pick up the call. If not, your parent will hang up. The call charge for making call is minimal but they can reach you in a very convenient way. For making long conversation, you may tell them to hangup first and you make a call to them directly via other means at more economic way.
From the technology point of view, we may spend some time to explore the real call-back feature using Asterisk.