Does a channel tuned with your VCR show on the TV? If so,
pressing "PLAY" on the VCR's remote should replace the tuned
program with the program being played back. If not, find out why
you can't get the VCR tuned program to appear on your TV. That
will solve your playback problem, too.

Absolutely correct, in principle.

I'm also puzzled how changing the /cable channel/ lets you select the
channel to record on the VCR. Unless you have a video output from the cable
converter feeding the VCR, you need to select the channel to record on the
VCR itself.