Tyson, You need good bushing's that support the rear end, Good geometry to start with, things like ensuring the rear is square with the centerline of the car and all angles are correct.
With a little tuning. if there are adjustable, And stiffen the chassis than you will be well on your way to long burnout's with out the shakes. Sounds as if you just have too much flex into the chassis. If applicable, build a roll cage. If not, than things like frame connectors and sway bars and other stuff should get you what you want.