I wasted a couple hours on the pry method and got nowhere. Just gouged up the aluminum control arm. What worked for me: get yourself an old time pickle fork (ball joint separator) and hammer it in between the ball joint and the steering knuckle. Don't pry, just hammer it straight in. When you get the ball joint to move a quarter inch or so, then put in a big open end wrench between the pickle fork and the bottom of the steering knuckle, then hammer again to get the next quarter inch of movement. I finally needed about three wrenches' worth to get the joint apart, but it worked. The first one I did, since I tried prying first, I tore up the boot pretty good, and it can't be replaced. The second one, just hammering, the boot came through ok. Putting them back together, lube the new ball joint shaft generously with axle grease and it will go in once lined up. Make sure it's all the way in so you can get the bolt back in place. Good luck.It may be the play they detect is the ball joint because that it is integral to the control arm. It is not a separate part that can be pressed out.
The ball joint stud is almost two inches long. The first inch is easy, the rest almost takes two people leaning on it. Pry on anything that looks solid. There was a you tube on replacing the cv joint axle. See if you can find that.