'14 Fiesta back end wiggling/wandering over bumps

Sedan, has 180k miles.  Checked it for obvious damage.  Wheel bearings feel good, fresh-ish front tires, pretty used rear tires.  Did a little searching around but base model Fiesta owners don't seem to have any issues.  Tires are Falken SN201, 185/60R15...yeah, they are cheap, that's what they have going for them.  

6 months ago:  driving down to CLT in the rain was really sketchy.  Car was wandering on I77.  I just assumed it was really bald rear tires (almost slicks, I'm cheap...) and/or tram lining on interstate.

2 months ago:  Got new tires after that CLT trip, put them on the front and moved the (pretty decent) front tires to the rear.  Drove down to Daytona and in the raining time on I73, it was a bit sketchy.  Not really standing water, but notched up the "issue" to just the wet roads

This past weekend:  My wife drove it (in the rain) and said the car was "very wiggly".  I drove it the next day, in the dry, and it did feel weird.  Very windy yesterday, so maybe that contributed.  I checked the wheel bearings, made sure all wheels were tire, checking bushings, tie rod ends, etc.  Nothing amiss...

Anyone else have experience like this?  Is it just a case of bad tires with a chassis that is known to be sensitive to tram lining?  I will be getting some different tires for the car soon, so we'll see how that goes, I guess.  

Try put the new tires on the back.

Worn out bushings. My 2004 Focus wagon was absolutely spooky in the snow because all the rear suspension bushing wear egged out.

Maybe try a quick string alignment to make sure you don't have noticeable toe out in the rear. That can make things a little squirrely. If that checks out then as stated above, check for sloppy bushings. 

It's likely toed in or out, either because a bushing has worn, or a limk is bent somewhere.

Too much toe will make a car spooky as hell, particularly when there is variable traction side to side.

I'd certinally check alignment but my first thought is shocks.

Lots of tire changing/moving...properly torqued lug nuts?

John Welsh said:

Lots of tire changing/moving...properly torqued lug nuts?

No wobble on the wheels.  Pulled them all to make sure they were seated well.  Torqued again to 100 lbs.  

Bushings and struts/shocks.

if it's got that multilink trailing blade rear, i'd look at the forward bushing in the trailing blade, where it attaches to the chassis.  On my 2018 escape that bushing completely de-bonded from the sleeve and the shell, at around 55k miles.  Significant dynamic geometry changes and hilarity ensued.