Shifting Rear End

I have a 2004 Kia Spectra I purchased 2-3 months ago. It drives good on smooth surfaces, no issues. However when I hit uneven surface or pot hole the back end seems to shift from side to side for about 1-2 seconds then recovers. I looked under it and didn't see anything broken. One tire looked worn so replaced it. Was told it needed new struts, so replaced all 4 struts and mounts, but it still does this same shaking when you hit a bump or uneven surface. I jacked it up and tried to wiggle the wheels, but nothing loose. Didn't see any brake dragging. It doesn it even if you don't have brakes on. Any thoughts?

I have a 2004 Kia Spectra I purchased 2-3 months ago. It drives good on smooth surfaces, no issues. However when I hit uneven surface or pot hole the back end seems to shift from side to side for about 1-2 seconds then recovers. I looked under it and didn't see anything broken. One tire looked worn so replaced it. Was told it needed new struts, so replaced all 4 struts and mounts, but it still does this same shaking when you hit a bump or uneven surface. I jacked it up and tried to wiggle the wheels, but nothing loose. Didn't see any brake dragging. It doesn it even if you don't have brakes on. Any thoughts?
Did you try moving the rear wheels in and out?

Yes.

As it turned out had a tire that looked good, but apparently had a busted belt or something because when I moved it the problem followed. So replaced the tire and now am back in business.

Thanks