For a quick fix, try playing it in the second player and recording it on the first one, so copying the tape. This should produce a working copy for the first machine, because it should be able to play what it recorded.
If it works fine in one player but not another, this is probably cause by some misalignment on the audio section of the tape. If this it the case, it will be specific to the video cassette itself and not the footage. The newer player will probably be able to play the tape despite the glitch, in the same way some older CD players can't play home-written CDs.