SO, I have an 06 sonata 277K miles with the usual creaks and groans. I fixed that with new upper/ lower control arms, tie rods (inner/ outer), and links. It feels pretty good when driving now, all tight again. Now I just need to do the shocks struts blah blah.
Now for the problem.
After doing all this and getting the allignment done. The wheel is off to the left a couple degrees, BUT IT DOESN'T PULL. Just want to be clear.... When I break, the wheel goes strait and the front end shifts to the left real quick, but then continues to break strait. Now that I am stopped the wheel is strait and when I hit the gas the wheel kicks back to the left a degree or two and the front shifts to the right. OR if the hold the wheel it will accelerate to the right.
When I am driving on the interstate, it goes strait and doesn't pull at all. I was thinking it might be the breaks but it doesn't keep pulling, it is only for a second. I know I need to replace the wheels, one is worse than the other. Could that be it, or did I damage something in the rack putting the tie rod end on?

 

Picture this,
What moves when you accelerate and what moves back when you apply the brakes.
It does sound like there is something loose in the steering system that when torque is applied to the wheel by way of the half shaft from the differential to the wheel hub the tie rods are allowing the wheel to move more than normal. With the wheels off the ground , motor running in park, parking brake applied, if you try to move the wheels holding at the 3 and 9 o clock position, there should be NO ply in the steering system. Are the rack mountings all tight, no looseness?

 

I didn't try this with the car on. I did try it when I had finished and couldn't move anything. It was all super tight.
The thing that doesn't make sense is that it only lasts for a sec., not even a sec. Almost like something is binding then it gives, until I break or start from a stop. I am going to lift it up and check things out again, and chance the sway links. They ones that I got had a greese fitting on them that was hitting the body sometimes so I took off the fitting.

 

Something doesn't sound right,
I know this should not be possible , but,,,,,,,,,,,,,,,,,,,,,, when you installed the tie rod ends into the steering arms on the wheels, were they supposed to go in from the top or up from the bottom on the steer arm of the wheel? It is usually a tapered fit , but sometimes strange things can get done.

 

LOL I know those are right.... I was putting one of them on at one point and like......that's not going to work that way, so I had to redo it. I some things to do today, so I don't know when I will get a chance to look at it.

 

Here is something you might try,
Have someone move the steering wheel back and forth while you look at the steering linkage looking for any looseness.. You can do this with the motor running to take up any movement in the power steering hydraulics, just make sure it is in park , and parking brake applied. The wheels have to be on the ground to do this.Just be careful.
Would like to know what you find, thanks.

 

Can you get someone to follow you and watch the rear of the vehicle when this happens?

If something is really loose in the rear and the body shifts , the person following you will see that right away, the vehicle will seem to be "Dog tracking".