Re: de frente vs de reojo
De reojo is out of the corner of one's eye,
not from a corner which would be something like del rincón.
You could say:
He was looking right at it and I was looking at it out of the corner of my eye.
Also, in English we would use capital letters at the beginning and periods at the end of what appears to be four separate sentences in your English translation:
We were alone in the living room which was also the dining room. I was sitting at the table with a napkin over my lap and he was sitting on the sofa with a dwarf rabbit in his hands. Both of us were watching TV. He was looking right at it and I was looking at it out of the corner of my eye.