More than likely the problem is with the power steering Rack & Pinion assembly.
The R&P assembly has a spool valve that directs the hydraulic pressure that the power steering pump provides to a piston in the R&P assembly. And that spool valve is controlled by turning the steering wheel.
If the seals on the spool valve are worn, it can cause the steering to work fine in one direction, but not in the other because the seals are leaking.
But if you step on the gas so the power steering pump builds more pressure, it overcomes the leaking seals.