I bet when the movement was really jerky during the original recording, the video heads were also being jolted, so the signal recorded onto tape wasn't quite stable.
TVs etc can cope with slightly unstable cards, but capture cards can't. Read all the information here about Time Base Correctors (TBCs) - you'll need one to capture this footage. Either built into the playback deck, stand alone, or built into the capturing device. Currently, it seems you don't have one anywhere, so can only capture stable footage.
Cheers,
David.