Yes, it skips Antietam. Surprised me, too.
The movie is about repelling Northern invaders (see my earlier comment about the Confederate apologist tone), so you can see how Antietam wouldn’t fit the theme.
Also, in fairness to the filmmakers, I think they focused on Fredericksburg as a counterpoint to Gettysburg. In Fredericksburg, the Union forces bravely charge Confederates positioned behind a stone wall; at Gettysburg, it is the Confederates making the hopeless charge. (And remember that at Gettysburg, the Federals chanted “Fredericksburg…Fredericksburg…”)