If the tapes are quite worn or old, then the weaker signalling between frames or scanlines can cause the picture to wobbly like an off-tune TV channel. TV’s tend to use a differetn method to display a picture compared with how a VCR or many other recorders capture the picture and this is one reason why the developers of copy-protection measures can interfere with the signalling to affect recording devices, but not TVs.
Even though your tape may have no copy protection on it, poor signalling can still affect how another device captures the image. I seen a similar issue when playing some VHS tapes through my PC’s capture card.
If your VCR offers manual tracking, you could try to adjust the tracking in one direction a small bit and then try another recording. If this does not help or makes the recording worse, then try the tracking in the opposite direction. Even though a small adjustment in the tracking will likely not have any affect on the VHS playback picture, it could make a difference on the recording.
The final option would be to get a video stabiliser, if available in your area. This unit takes the source image and strips off the signalling between scanlines and sometimes even the vertical blanking scanlines between frames and then replaces these with its own signalling (and blank vertical blanking scanlines). These are usually intended for improving VHS to VHS copies, however they will work with other recording devices such as capture cards, DVD recroders and TV’s that are affected by poor signalling.