Even more connection options
Basicaly using the RCA connections from the cable box into the VCR and then VCR A/V out in to the 1050 gives you the best transfer of A/V signals when you want to record - or - listen to your 1050, since you have made this connection you may as well deliver the best possible A/V signals available (RWY) from the VCR and cable-TV into the 1050.

Sounds like you are - routing a CoAx cable out from the cable box to the VCR and then connecting another CoAx cable directly to the TV and then using the TV's audio out jacks to connect the TV's audio back in to the 1050. The problem is that the CoAx cable coming out of the cable box degrades the stereo sound, the stereo signal is further degraded by running CoAx from the VCR to the TV. The CoAx connection delivers the lowest quality audio signal to the TV. By taking the audio out from the TV at this point gives you lowest quality sound that you can supply to the 1050 when using the TV, Cable box or VCR.

Per Charlie's suggestion, Using the 1050 as the audio source selector and video switcher and letting the TV simply serve as a video monitor. By using the RWY or RW-S-vid interconnections will give you the best overall audio and video performance from all sources.

Another nice thing is that you can still leave the CoAx connections between the CB-VCR-TV should you simply want to turn on the cable box and TV to watch the news - etc - or a video tape without running the stereo in order to have sound.
The A/V jacks and CoAx are both delivering signals out, It does not matter whether they are connected to another device or not.