Before I started OWB, Vats worked perfectly normally for me, even with the weapons that are now giving me trouble. I've tried turning OWB off, and reinstalling the game, but so far nothing has worked. I've also tried starting new games, which have so far worked fine, but I haven't run any of them through OWB yet.
One idea I've found on the internet is that this bug is caused by the recoil animation triggering early, which means that the gun is fired at an angle away from the original target. I can't vouch for it's authenticity, however, and I don't know what practical impact that would have if it were true.
Does anyone have a solution? I've spent a lot of time searching the internet for a fix, but the only one I've found that described itself as solving this problem is a mod which is no longer available for download.
If it's important, my copy of the game is completely unmodded so far.