Change your connections this way:
1. From your cable box directly to your TV: use the cable box component output jacks (5 cables) or better, an HDMI cable if the box and your TV have HDMI jacks. You'll get far better video, especially if you've subscribed to an HD channel package.
2. Connect the coaxial RF output jack of the cable box to the antenna jack of your VCR. Connect the coaxial output jack of the VCR to the antenna input jack of your Sanyo. --or-- Connect the VCR's composite output jacks (yellow-red-white) to the composite input jacks on your Sanyo. Either way would work.
3. Set your cable box to output either analog channel 3 or 4 on its RF ouitput jack. Set your VCR to the same channel and leave it there permanently.
4. You can now record anything the cable box receives via the VCR. Just set up the timer in the normal manner. To play back a tape, select the proper input to your Sanyo (antenna or composite) via its remote.
5. When not watching something from the VCR, select your component or HDMI input with your Sanyo remote. You'll like the picture a lot better than what you've suggested above. Good luck.