I have an 88 camaro with a manual transmission, I like to drift around corners or do burnouts but alot of the time when I drift the whole car shakes when I go sideways. I've read something saying rear suspension might be causing this, i've only been able to find one video that shows what im experiencing but it's on a toyota corolla:
If anyone can help me that would be great, it doesn't always do this and it's not as bad when its wet out but I know its not my tires because I've gone through 2 sets of tires and nothing has changed.

 

wheels
driveline
pinion angle
unbalanced engine

No one can point to what the issue is, you need to become the detective and figure it out.
easiest is put on different rear wheel/tires on and see if it changes
from there, everything will be trial and error until you find it

 

i recently replaced both my rear tires because somebody slashed them, it hasn't changed so I know it's not my tires. My engine is also new so I doubt it's that, I think it is some suspension component but if anyone can tell me their idea of what it might be that would be very helpful. could blown out rear shocks cause this?

 

Any bad bushing can cause this besides all the other possibilities. It is caused by an oscillation. Basically your tires are loosing grip and immediately gain grip again then repeating the process. Have a friend wiggle the rear body of the car back and forth while you lay underneath watching every mount and bushing. Something is loose. It might be all just wore enough to contribute.

Also check for a bent wheel or axle.

 

i said install new wheels and tires.
you replacing just the tire means nothing if your wheel is bent.
how about the axle shaft it could be bent too

 

I had issues like this when i started to dial in my suspension. I had full poly bushings and solid trailing arms w relocation brackets/panhard bar/torque arm. I replaced my trailing arms w adjustable ones w roto/heim joints and adjusted my pinion angle and now it rips. My issue was a mix of poor pinion angle and binding w poly joints. The roto/heims are much better. If you have an original suspension then something is loose/bad bushings or both. Sticky tires will exaggerate this.

 

^That^

 

Aside from new rear tires, we know nothing of your suspension setup. Some information about what you have on your car would be very helpful.