Break the tapered stud as normal, then with the lower control arm hanging down, support it with a stack of lumber or with a really beefy jack stand, right under the arm as close as possible to the ball joint. Remove the dust boot, then you can pound on the housing of the joint, alternating side to side, to drive it out.
To run the new one in, tap on both sides on the bottom to get it started, then use a pair of c-clamps as though you were going to pull it in with them. Just make the clamps as tight as you can by hand, then tap on the housing a few more times. Hard or heavy pounding won't do it. That will just make the joint go in crooked. Alternate tightening the clamps and tapping on the bottom. Tap only on the thick outer part of the housing, not on the center disc where the grease fitting screws into.
If the joint goes in too easily, the hole in the arm is stretched. The arm can be replaced for that, otherwise it not uncommon on other models to add a couple of tack welds with a wire-feed welder to ensure the joints stays in place.
One thing to be aware of incase it still applies to your model year, on the older ones, it was normal to see the lower ball joints have a good 1/8" of vertical play when checked while they were "unloaded". New lower joints from Chrysler had that play in them right out of the box. That was acceptable and normal, and it did not cause a clunking noise When I asked a Napa rep about replacement joints at a class I attended, the question was, "how do I know if that's an original Chrysler joint with acceptable movement, or a Napa joint that wore out and developed that movement?". His reply was an aftermarket joint can be allowed to develop that same vertical play, even though it didn't have it when it was new. Regardless of the supplier, no ball joint can ever have sideways play.
This goes back to when I was the suspension and alignment specialist at a very nice Chrysler dealership through the '90s. If you only have vertical movement in your lower ball joints, consider asking the people at the dealer's parts counter if that is still acceptable for your model year. A lot of mechanics at independent shops will argue that it not true, and for all other brands and models they would be right, so don't fault them for saying yours are worn. Remember, that's only for vertical play on the lower, "load-carrying" ball joints. The uppers must still have no play in any direction, just like those on other vehicles.
You might find this article of interest:
https://www.2carpros.com/articles/how-to-release-a-ball-joint
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Sunday, July 10th, 2022 AT 7:18 PM