If you grab the tire on top and bottom and can move the bottom and top in and out...then yes the lower ball joint is gone. Replace both side of the car. You need to cut or grind off the three rivits that hold the ball joint to the lower control arm ( makes it easier to remove ) anyway. Undo and remove the pinch bolt and install the new ball joints with 3/8 by 1 1/4 grade eight bolts and lock nuts.While you are there...grab the wheel or tire at 3 oclock and 9 oclock and see if you have any play in the wheel that way as well. If you do...then you also need to inspect or replace your tie rod ends. Easiest way to check the lower ball joint is to jack up the car...put a bar under the tire and lift the wheel up and down keeping your one hand on top of the tire. A wheel bearing would give you a noticeable humming or whirring sound from the front end while driving.I think your problem is the lower ball joints.
