Removing a stuck pedal
Your best bet is to use mechanical advantage to your benefit. What you want to do is line the wrench up with the opposite crank, so that your hands are as close together as possible, now straddle the frame and force the two apart. Here's an image from Park's description of how to remove a pedal that illustrates it well:



The worst position for the wrench is 180 degrees opposite, so that the crank and the pedal are still parallel, but opposite. It will be almost impossible to remove a pedal in this orientation.

You are correct that the drive side pedal will have a normal thread, and needs to be turned counterclockwise for removal.

It generally takes a lot of force to remove pedals, because they tighten themselves as you ride due to precession. If you find this method still isn't working, refer to Scott's answer about lengthening your tool to gain leverage.