Here are 2 videos that show what is going on for a better idea: https://youtu.be/LEGJTefVHO8 https://youtu.be/E5WQf2f83ZA
It looks the assembly is tight but the toe is way off. Replacing a tie rod end is pretty key to that. I’d say it is toed way out. Both front tires are pointing out rather than being parallel. You need an alignment in any case with the parts you replaced.
Concur w/MM above, presuming nothing is obviously loose or installed incorrectly, it’s going to be hard to diagnose any problems you may have until the you get a 4-wheel alignment done. Or at least driveway-ball-park the straight ahead alignment (camber and toe) using strings and levels etc. It may well be that once the alignment is correct the other problems will disappear.
The only other guess I can come up with is that perhaps the suspension system is stuck/binding b/c the wheels were lifted off the ground. On some suspensions designs — may not apply to the Taurus – but on some anyway the wheels must be prevented by some means from just falling as far as they want when the car is lifted by the chassis. If the wheels are allowed to hang free, the suspension system might not be able to bring it back into the proper geometry when the wheels are back on the ground. There is often a noticeable change in the rocker panel height off the ground when this occurs.
I got it taken in for an alignment (the toe was indeed super far off) and with that done everything seems to be fixed. I guess that’s all it was. Thanks for the input everyone!
Thanks for the follow up!