Why I said tires? I assumed you had already had checked\tested the components of your
suspension and steering. You mention new ball joints and wheel bearings which to me suggests you've done or had done the basics of the process to solve your problem which apparently hasn't solved your problem. Am I right in this? What you haven't addressed is if your
suspension and steering is stock or if the tires you've put on are the recommended size? It's important information if what you're running isn't stock. Again, I assume everything is stock if nothing is said to suggest otherwise. To try and help with a posted question any answer has to start from some reference point to suggest anything useful. More than likely no one here is familiar with your car so assumptions have to be made. As an extreme example, I know of 4WD Mustangs with 40" tires but I don't think anyone would default to an assumption that this would apply to your car.
About tires, the age of your tires doesn't make any difference. Unfortunately a tire's "lateral tire deformation" is a spec that isn't required to be stated and outside of the realm of racing tires I don't think tire manufacturers are required to share the information of testing results that go in to lateral tire deformation ratings. This is about what is referred to as "sideslip." Lateral tire deformation is a vector measurement of linear, transient and saturation forces as tested against
suspension deflection under various conditions. At one time I worked out of a place that had a test track that was often rented out for tire testing and learned that typically most tire companies all use the same list of vehicles for testing so the different tires from the different companies have tires with ratings that can be fairly compared with the ratings from other manufacturers.
All of this amounts to new tires really means nothing for the problem you describe if the tires you have don't match how your is set up. There is a lot more to tires than how long they last, the load they are rated for and the amount of predictable traction a tire offers under various weather conditions. If this was all there was to a tires specs, a $400 Bridgestone wouldn't have much on a generic $129 tire but we know that's not true.
What you're experiencing as described assuming everything is mechanically sound is an understeer lag in your steering due to sideslip. That's tires resisting a change in direction. They can't respond to the demand put on them by your
suspension when you turn at speed. Another possibility although highly unlikely if they were mounted at a tire shop is you have directional tires that are on the wrong side of the car. This usually involves the same problem though with centering the tires coming out of a turn. They would resist any change in direction which you don't describe. An induced over and understeer similar to driving on ice.