Torque steering or pulling under acceleration

To test if the car is automatic put in a low gear and accelerate hard and see what way it pulls. Then let off accelerator fast and it pulls the opposite way something is loose in suspension. Bushings,brackets,welds ect. I cant think of anything in the trans that would cause a pull.

Check:

Motor Mounts
Transaxle Mounts
Front CV Drive Axles
Loose or Worn Front Suspension Parts
Steering Rack Mounts
Steering Rack Inner Tie Rods
Top Bearing Plates on Struts
Do Some Front Brake Work

Is it a Standard Trans ?
Clutch Could Be Worn

take in for front end alignment. and yes there is a trans mount

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try getting motor mounts checked or struts or wheel bearings , start with mounts.

Sounds like the motor is out of alignment depending on how far the motor was moved, your pulling problem stems from the fact that the steering was probably dropped out to access the mounts so you now need a wheel alignment, hope this helps.

Get the engine mounts checked. A bad mount may allow part of the engine to lie on a body or frame part, allowing engine vibrations to become very loud. Torquing of the engine (under load) can cause the same type problems.

I have the same problem, but haven't replaced the half shafts. rotation and allignment done after both tie rods replaced Vibration seems to dissapear when letting up on the accelerator
Any help would be appreciated

If you are driving any front wheel drive vehicle, what you are feeling is called torque steer....sometimes it's from poor design but it can also be caused by a broken engine or transmission mount allowing the engine/trans assembly to shift under load or when removing load.
You can do a quick test by holding the brake down firmly and in gear, press down on the gas. have someone watch (from the side of the car ONLY) and see if the engine shifts. Do in both drive and reverse.
Be very careful when doing this that the car does not get away from you and do not hold power for more than about fifteen seconds at a time or it can overheat the transmission. This only works in automatic trans cars... for stickshift ones you need to move the engine with a long pry bar.

rack and pinion is the steering wheel joint, so if the steering wheel shakes or handling has decreased, then i would say it is the rp. , also check the wear on the tires for uneven wear, it could be alignment, does the steering pull to one side? it could be motor mounts just find the bolts and check em wiht a torque wrench, also inspect mounting bushings as well. to check trans. give it alot of gas to get past 35-45 mph and the shaking should go away at higher speeds, if it doesnt then its the trans missing "third".