Car shudders when I brake during highway driving?

That has to be caused by something that's rotating, in this case, the rotors. In the past, it was quite common to have them machined on a "brake lathe" to true them up, but there is a published legal limit for how thin they can be machined. That's called the "machine to" value. After that, there is another specification called the "discard" value. That allows the rotors to wear a little thinner and still be legal.

For some time now rotors are built very thin to start out with, to save weight, so it's not unheard of for a rotor to already be too thin to machine. Fortunately new rotors have come down a real lot in cost, so it doesn't make economic sense to machine the old ones.

There is one thing to be aware of with new rotors. When we make parts out of cast iron, we set them aside for three months to "age" before they get their final machining. Most new rotors now come from China. There's nothing wrong with their quality, except they don't let them age like we do. They get manufactured and shipped, then they age on your vehicle. It is common for them to develop a warp within that first 90 days. Most shops and auto parts stores will do a light machining on them for no charge to solve that. Those rotors will be fine after that. This has even been happening on some new cars.

If you're going to have a mechanic do this, let them check first before replacing, because you could end up with a similar pulsation with new rotors. After six years, I'd expect to find just one rotor is warped, but it's customary to machine both front or both rear rotors at the same time. They end up with a spiral cut, similar to a record album. Those grooves will wear down until the friction surfaces are perfectly smooth, but in the meantime, it affects the braking power. We like to see that be the same on both sides for even braking with no pull to either side during that break-in period. Think of wearing two different shoes on your feet. It can be done, but we typically like the two shoes to match so you don't walk in circles.

Let me know what you decide and how this turns out.