Turning XBox One/XBox 360 into a Nanny Cam

I want to SPY on my home and my baby. As a first time expectant father, I am thinking seriously about it. One solution I came up with is to leave Skype Open for a given account and keep the call active - but if the skype call gets disconnected -it would need an active user at the Home front to re-connect - and I prefer single channel not the dual channel of Skype.

I just want to know the suggestions or clever hacks that you have tried out to convert your xbox into a nanny cam.