The best and easiest way to separate the ball joint from the lower control arm is to use this tool:
The smaller puller on the top left corner is the perfect size to pull apart the ball joint.
Advance Auto rents them out. I just rented the tool kit this past weekend for $106 and I got my money back when I returned it. So you get to rent it for free basically..
You do have to be a bit careful with the tool though. Keep the castle nut on the stud but loose towards the bottom of the stud. When you set the tool in place, carefully and slowly turn the press little by little. If the ball joint does not separate after a few turns, make one more turn and leave the tool in place for a few minutes. This will allow the pressure from the tool to strain the balljoint and when you make one or 2 more turns, it should pop off and you'll be done. Do not rush it or force it. You will risk damaging the ball joint stud and then you're stuck replacing the whole ball joint... Not good. Just be paitient and be a little gentle.
I know some people have luck beating the crap out of the lower control arm/ball joint with a hammer and/or using a pickle fork separator. But I know that does not always work. Also, the pickle fork type separators can tear the ball joint boots which you do not want to do.