The rear end "jumping around" when hitting bumps etc would probably be caused by something else rather than sidewall deflection. Worn out bushings, long shackles, etc...A watts link or panhard bar would really help in this situation.
Where sidewall deflection becomes a problem is during cornering. The tire will tend roll over to the side. Causing slightly sluggish cornering and sometimes oversteer. It sorts feals like when you turn the wheel it takes the car a split second before it actually starts to turn. This can tend to cause you to oversteer.
Kinda feals like your tire pressure is too low.
A wider rim would help. Attached is a quick sketch I drew in MS paint. I've drawn the 2 extreemes... hopefully from the pic you can see that if you were to grab the tread and try to move it sideways, it'd be alot more difficult to do on the wide rim compared to the narrow rim.