Front end issues

Have you performed a suspension and steering systems inspection? Has the alignment been checked? If so, what was found?

You are describing something that is shifting between acceleration and braking. The more common causes of directional instability are a worn tie rod end and a sloppy control arm bushing. Control arm bushings used to last the life of the car, but for the past couple of decades they have been made from softer rubber so they fail quite often now. They can usually be identified by poking at them with a pry bar, but the movement needed to cause steering wander can be too small to see by eye. Then it will show up as wildly-changing numbers on the alignment computer.

The less-common causes of steering wander include excessive total toe-out on the front wheels, and incorrect toe and/or camber caused by sagged right height. Restoring ride height with new springs can correct multiple symptoms.

A brake pull must be considered too, but do not spend a lot of time on that until all other causes have been exhausted. Most front-wheel-drive cars use a split-diagonal brake hydraulic system so if one half springs a leak, you will still have one working front brake. Years ago with only one front brake working, the steering wheel would get torn out of your hands when applying the brakes. Today, "scrub radius" has been modified to the point that at most, all you will see is a tiny wiggle from the steering wheel. That also means you are less likely to notice a pull caused by a sticking brake. Additionally, you described the direction of steering as varying from driving over road surface variables, not just when braking. That points more to worn parts and mis-alignment.

Who did the inspection and found the worn parts? Something got overlooked.

Here is something you might consider. There is a tool you might be able to borrow or rent from an auto parts store that borrows them called the "Chassis Ear". It is a set of six microphones, a switch box, and headphones. You clip the microphones to suspect points, then drive around while listening with the headphones. You can move the microphones around to zero in on the source of the noise. Be aware that many mechanics have never seen or even heard of this tool. Suspension and alignment mechanics use it to find rattles, squeaks, and other noises.

There are multiple versions of Chassis Ear now. The older one used six wired microphones, so you had to drape wires into the passenger compartment. The newer one uses two of those, and four wireless microphones, and another version has six wireless microphones. The original version sold for $200.00 from the guys who drive the tool trucks and visit each shop once a week. You can find them for much less on Amazon.