The connection from the ATSC box from Karen's TV can be done either by coaxial cable (and both devices will need to agree on Channel 3 or 4 using physical switches) or by an RCA-to-RCA video cable.

Clarification. The RCA-to-RCA solution works but it's more than just a video cable. That signal is ONLY the video.

Such a solution (as an alternative to coaxial) requires a triple-RCA AV cable with yellow, red and white RCA connectors on each end.

I've used this. Video quality is inferior to using coax, but that's not an issue here.

- Evan