You might have what I have and that's a caliper sticking.

I also have a steering wheel "shudder" when the brakes are applied. I wasn't sure what it was. I did notice that as I applied constant even pressure, the shuddering would finally stop.

Recently, I went in and changed all my brake pads. I wasn't ready to challenge the shuddering yet because I simply wasn't sure where to start looking for the issue so I procrastinated on that for a little while but here is what I found changing the pads. Pushing the right front and both rear caliper pistons back into their bores was pretty effortless. The driver side front caliper? Not so much.

I actually had to use a c-clamp to force that piston back in while the others I used a light weight ratcheting hand clamp.

My prognosis is that the caliper needs replacing. The force it took to push that one piston back was easily two times or more greater than the other three. Can't say for certain but I am pretty confident that is my problem.

Maybe it could be the same with yours?

BTW - I wouldn't suggest anyone just replace rotors due to vibrations. Rotors are expensive and they can be easily checked for wear and runout. Make sure that has all been checked first before replacing rotors.

Cheers
Bernie