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Jess -- I agree with Hulot. The photo of the group is front focused, and the back row is OOF. The front row looks just barely in focus, and the entire shot needs more DOF for this arrangement of subjects. I don't see any lack from side to side in focus, other than the normal curvature of field issues.
I like the photos, and you do seem talented. But I do think you have either unreasonably expectations or technical errors, or a combination of the two.
Knowing just a little of how the sensor and mirror box is mounted to the frame, I don't see much room for misalignment unless the frame was crushed or skewed somehow. That would be a major misfit for all the exterior parts too.
I didn't catch if you were talking about the new 24-70L II or the original. Having used the new one a bit, I'd be surprised if there is anything major wrong with it, but it should be covered by warranty. The older one, well, I just sent mine in after trying the new version, and paid to have it adjusted. Now it has better IQ, but still no match for the new one, and definitely not a prime lens.
It would be nice to hear from someone more knowledgeable and experienced, like Roger.