jim.pat7 :
I apologize that I failed to mention my provider is Comcast xfinity. They allow me to rewind a show as long as I don't change the channel. It only rewinds as far as the time I started watching a certain channel. Sorry I didn't mention that.
Are you connected directly to the TV with the cable or are you going through a cable box? If a cable box, turning on the TV does not matter since what you need to turn on is the cable box. All the TV does is display what the cable box sends it. Just leave the cable box on, TV off, the issue you have is the rewind time. If you set a power timer on the cable box it will actually power it on but it will not "turn on", it will be at the basic mode where the clock is on. The only way to do what you want is to get someone to physically turn on the cable box or be able to change channels if it just stays on. If the remote app does not work outside the house, then you are out of luck unless you setup a VPN connection from the phone to your router. That may work, but will take a bit of work.
If you really really want to record stuff when you are not around, get the DVR option again.