The first thing I'd do is remove the drivers, run a registry cleaner [I use CCleaner for this sort of thing myself], and download a fresh copy of the latest drivers and reinstall them. If that doesn't fix the problem, it's a pretty good bet it's not a software issue.
Does the controller behave that way on an Xbox 360 or another PC? Does this bad controller only not work if it's used at the same time as the other controller, or does it behave that way whether it's used on its own or not? If both controllers were acting up when assigned to the second player I'd suspect a software issue, but if it's the same controller misbehaving regardless of which player is using it I'd have to say it's a hardware problem.
Try it out on another machine and see how it behaves. If you don't have a 360 or another PC to try it on, hook it up to a friend's console or PC. If it's acting the same way, it's probably the controller. You could also have a friend bring another 360 controller and try it out on your current setup. I suggest doing both.
If the controller works as it should on another machine and another 360 controller behaves like the one that is acting up, then there's a good chance that it might be an issue with the wireless dongle and not the controller itself. I doubt that will happen to be honest. If it was the dongle it would probably cause problems for both controllers. Still, it's better to err on the side of caution and try it out anyway just to be sure.
Honestly, if one is behaving fine and the other is not, it's probably the controller. I doubt it's a driver issue if one works as it should and the other does not. There aren't settings to adjust with the 360 controller drivers. It's just a plug and play program and there really isn't anything to do to tweak it.
You might want try to crack it open and maybe see if cleaning the inside might help. It could be that the interior got some gunk on it or a part is sticking because of build up or some other substance that got into the controller. The worst that could happen is it gets more broken than it is.
All you need is a small phillips head screwdriver, some rubbing alcohol, and a couple of cotton swabs. Clean the contacts for the buttons and see if there's any build up around the analogue sticks and d-pad contact points. If you're careful it isn't difficult to do.
Two important things. First, there is a screw under the bar code sticker inside where the battery pack goes. Just use a knife to get it up and carefully peel it away. You can replace it when you're done if you wish, but there's really no need to do so once it's off because just opening the controller voids any sort of warranty it might have anyway.
Second, ground yourself before handling the circuitry inside. It won't shock you, but static electricity from you can damage it beyond repair. It's not terribly likely that it will happen to be honest, but it's better than regretting not doing it later.
If you need a guide just Google it. There are plenty of online resources that will give step by step instructions with images and even video. Most of them are guides to disassemble the controller for painting, you shouldn't need to disassemble the controller completely to the extent most of the videos go to. The first few steps of taking the controller apart should be enough to allow you to clean the buttons, analogue sticks, and contacts with some rubbing alcohol. Just don't forget to let it dry before you put it together.
Good luck with your issue.
