Here's how you get the pigs.
First, you need to disable the mines on the left when you enter the area. If you do not do this the pigs will path right into them and you will fail the quest.
Once you do that, you need someone with ranks in Brute Force. Angela Deth has more than enough when you get her, I believe, and go up to the farm. On the far right side of it there will be a gap between the farms fence and the rocks. At the bottom two rows of corn past that gap there will be a section of the fence you can use Brute Force on, and just inside and above will be another breakable part of the fence. Go through the second hole you broke and follow the path behind the farm all the way to the back of the pig pen. Break the fence there and the pigs will make a run for it. If you cleared the minefield, all three pigs will make it.
There are other sections of breakable fence when you're running around the back of the farm. I do not recommend breaking any of them, as the pigs might path through those broken sections, and right into the foremen.
When the pigs reach the travel marker on the map, go back to the farmer you got the quest from and turn it in.