93 Honda Civic, vibration/slamming,pulling

[AtruEulogy]

Hello everyone. First let me tell you what i have,

93 civic hatchback 5speed, swapped with a 96, 1.6L non vtech motor.

and a 4stage LSD Transmition.

On crappy, Skunk 2 Coilovers which i am replaceing with stock suspension.
on 14" stock steelies.
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Car was handling fairly well last week, with the exception of ruff ride and occasional vibration when you hit a good pothole or bump in road the steering wheel would vibrate (death wobble) but that is not the problem im trying to fix.

The problem that concerns me is, The torque of the car pulls the car to the right slightly when gassing hard. But as it pulls to the right, the steering wheel jogs to the left. The steering wheel travels left when car pulls right. It never did this till we had a bad snow storm the other day, and i got stuck in about a 2 foot bank of snow.> No ruff impact. just drove into it to go through and didnt make it through. tire spinning packed with snow.

So after all the snow melt and roads are back to normal. im driving and noticing that when i gass hard the car pulls hard to the right, but the steering wheel pulls opposite direction a inch or so.. and as you let off the gas the wheel goes back and the car settles back straight. Now normal non torque take off the car drives straight as an arrow.

Just rides Ruff. has a vibration when hits bumps and hard turns.. and now pulls opposite of the steeringwheel. BUT NOTE THERE IS NO PLAY IN THE WHEEL> ITS TIGHT>. you turn a inch to the right. the car turns to the right. there is no loosness to turning. just pulling and pushing going on..

Any ideas where to start looking, ???? would be helpfull.... I have a feeling my ruff ride will be solved with new shocks and springs.

and im thinking the pulling of the steering is due to busings or tie rods or something im not sure...... havent looked under car yet.. Before i do, some advice on what to look for would be great..

THE FEELINGS IS REALLY bad on the highway.. cruising speed at 65, slight vibration, and if you put the peddle to the floor in 5th or even 4th gear at 65, the car pulls very hard to the right.. and i you let off the gas it goes back to the left. causeing some serious adjusting needed to not side swipe cars or drive in other lanes... what causes this?