My steering pulls to the right when i accelerate and pulls to the left when i slow down, the tracking and balancing have been done twice, there has been Tyre rod has been change and serviced. Need help as the mechanic and the Tyre company are stumped

taking it for granted that there is no brake binding issue/sticking calipers or any wear in suspension bushes, particularly lower arm bushes...that these have been checked and cleared as ok..then..

sounds like you could possibly have something siezing up

it could be anywhere in the steering/front suspension

way i would do it, is jack the car and turn steering by hand, at the wheels from one lock to other...then disconnect either track rod end, and check lock to lock at each wheel...if the wheel thats still connected feels noticably lighter, then take a very close look at all the joints of steering/suspension for sticking/corrosion etc on disdconnected side...not forgetting the disconnected track rod inner and outer joints...

can leave the track rod off, but repeat procedure on opposite side..plus compare the effort needed on both wheels with steering disconnected...

if all ok, while disconnected have a very close inspection of column..cant remember, but if there is a universal joint in the column that could be where your problem lies

hope that helps, only a suggestion but if it was me, thats what i would do.