Whenever I go over the slightest bumps on the road while accelerating, the ***-end of my car wiggles and sloshes very annoyingly. What suspension mods do I need to keep the rear planted while going over bumps? Upper/Lower control arms? Panhard bar? Thanks.

 

Full length welded subframes and lca's.

 

the rubber bushings in your rear end is the cause. They are likely worn out causing excessive movement. You can swap them out for stock stuff or upgrade to urethane bushings.Its the bushings in the upper and possibly also the lower control arms. check the swaybar bushings too.