I've noticed this 2-3 times already, but during long sweeping turns- sometimes, the car feels wobbly/unstable. Say, during left turn cloverleafs, it feels like the weight is being shifted from the front left tire to the rear right tire several times until I completely let off the throttle or once the turn is finished

It feels annoying, like sitting on a table with 1 short leg. Could it be an alignment issue?

 

I had a similar feeling after a bad alignment was performed. I attributed it to dissimilar camber settings in the rear. Getting an alignment exactly to spec (no tolerances) should fix the problem. Make sure you are sitting in the seat during the alignment too. Also, check that your cold tire pressures are the same all the way around.
This all assumes that the road surface you drive on is reasonably consistent.

 

I had a similar issue, but hopefully it's not the same. When I took my car in for alignment, the guy decided he could get a little more adjustability by loosening the ball joint on the suspension.

So, yeah... every time I went into a corner, the tires would stay planted, but the car would wag its tail. Needless to say, I haven't been back to that shop again.