Some owners have, indeed noted power-steering problems in this model Commodore. That said, this is a very common model, so some problems are to be expected as they with most other makes and models.

The most common problem seems to be a squealing noise when the wheel is turned. That’s often due to low power-steering fluid level (check the dipstick at the top of the reservoir under the bonnet). If the level is low, you need to start looking for a leak as this is a sealed system and shouldn’t need topping up over time. Leaks can occur in the pump itself, the steering rack or the plumbing that joins them.

A vibration through the wheel or a fluttering sensation can often be caused by air trapped in the system. With the engine running and the car in Park, turn the wheel slowly from lock to lock a couple of times., That’s often enough to purge the air and return the steering to a nice smooth feel.

Some owners have reported an improvement in their power-steering by draining and flushing the system and adding new fluid.

In the old days I might have said it was due to fuel surge, but that doesn’t happen with fuel injection. It could perhaps be a connection in the wiring that is separating when the car swings to the left. It needs investigation.

If you're towing on the flat and not overloading the transmission you might get away without upgrading to the cooling package, but if your short distances include hills you should upgrade it. If you don't you're putting the transmission at risk of overheating and being damaged.