I have not seen that before. Is the style supposed to look rustic?

How does the curve compare to the straight lines? Are they consistent in being uneven?

expansion joint so concrete doesn't crack.

Yes. I think the OP expected an expansion joint (or at least I would have), but the joint is not a smooth line... It is rather jaggedy.

I wouldn't be happy with it, and I know that there are contractors who can do a much better job. Did you see any of their work before you contracted them to do it?

I am not sure what can be done at this point about it though...

The straight lines look great. About half of the circular driveway has this jaggedy look and the other half looks pretty good. I'm not happy with it but like kirkhall said, at this point not much can be done. And I definitely have seen lots of their work before and it never looked like ours turned out.

Since the outer edge is stamped and looking somewhat natural, the "wobbly" lines carry out that look. A perfectly smooth line might have looked out of place.

Well if the straight lines with the same edge looks good then that looks like a subpar job to me.

They can cut it out and redo that section of concrete at their expense. It does mean you'll end up with one more expansion joint in the middle of the driveway, but it may be ok depending on where they place it.

I would think over how you want it resolved. Do you mind them cutting the driveway and patching it and if so how you wouldn't mind another expansion joint and where, or do you just want them to knock money off the price and you'll live with it as is?

Putting that radius line in the concrete isnt easy. That is done with a special hand trowel and has to be free hand. While you are doing it you are constantly running into buried stones that you cannot see that are bumping the tool as you go making it hard to stear. At the same time as having the joint line installed they have to deal with the stamping to keep up with your design and coloring. All while the concrete is setting up. The straight lines are struck using a board as a guide for the trowel and are much easier to get straight.
I think they did a pretty good job......considering the design.
You will regrett having a partial tear out and do over.
Thats a another story...

~Al

Dry cutting the concrete soon after it set could have achieved a more even look. See, for instance, this video using only a circular saw with a diamond blade. Scoring the concrete while still plastic, as in the picture below, ensures it won't crack but is not as even as a drycut.