Wobble or Shimmy at Slow Speeds

My wife's XJ has a wobble or "shimmy" when driving at slow speeds (under 15 mph) and becomes less noticeable (basically nonexistant) at speeds above that. We have a gravel driveway with 12" potholes in it and the wife drives it like she stole it.

I'm definitely a newbie at this. Where should I start looking? Could it possibly just need an alignment?

Check the lug nuts. Alignment won't fix this. Check ball joints or bent rim.

Checked the lugs, it's not that. I'll check the ball-joints and rims.

Thanks for the help

Just checked ball joints and rims, both are fine. I notice now she's broken both the front driver's and rear passenger's side shock mounts. Could it be this by chance? I'm thinking it isn't but it's worth asking.