I would check the control arm bushings first.
When worn out, would allow some "play" that would be especially noticeable as a violent "shimmy", especially when cornering. That can't be corrected by tire balancing.
The OEM bushings are rubber but I think there are some aftermarket urethane units ??available??
Might be a good idea to get an alignment performed after installation...
2009 ML350 (84K) - Family vehicle
2001 CLK430 Cabriolet (71K) - Wife's car
2005 BMW 645CI (124K) - My daily driver
2012 Mustang V6 (60K) - Daughter's car