Q: Rear suspension arm bushing has play

I have a vibration that occurs at ~55mph or over but only when veering/turning left at these speeds. I also feel what seems to be the same vibration from the same area (rear of car) when braking at these speeds. I hear the braking noise at lower speeds than the vibration occurs also, though at highway speeds I feel it in the pedal and at lowers speeds it's more like just a 'chatter'. 2 weeks ago it occurred when turning right. I have had 4 new tires installed and balanced, a 4 wheel alignment, new pads/rotors in front and new drums/shoes/springs in back. Now it occurs when turning left (though I still feel a very slight vibration when veering right but it's barely noticeable at all). I have discovered that the rear wheels (source of the noise/vibration) have some play when I hold them at 3 and 9 and move them in and out. I can see where the rear suspension arm meets the axle carrier there is some play in the bushing(~1/8 inch) when moving the tire. Could this be the cause?