Another question about Lee's strategy

As Lee explained to Longstreet as he briefed him on the plan on the morning of July 3, "The enemy has reenforced on both flanks. He must be weak in the center."

Fatally flawed logic, but when you're the Army commander and a full General (the equivalent of a 4-star in today's US Army), even a Lieutenant General and Corps commander (equivalent of a 3-star) like Longstreet can have trouble convincing you of its flaws! Michael Shaara wrote the original book as a Greek or Shakespearean tragedy set in the Civil War, and this is the point where the heroic figure's hubris brings the tragedy and woe upon himself.

There are several parallels with Waterloo. What was Lee thinking?

Lee's original plan for Day 3 WAS that there would be an attack on the (Confederate) right in morning, and an attack on Culp's Hill was planned for the same time. But two things caused Lee to abandon that idea and go up the middle. First, the Union got the jump on the Confederates at Culp's Hill and attacked before the Confederates could, driving them back off the hill and wrecking the first prong of Lee's plan. The second prong - the attack on the right - was wrecked because for some unknown reason the orders to do so were never properly conveyed to the field, and even if they had been properly conveyed, the loss of Culp's Hill would have destroyed any chance of an attack on the right working.

After all this happened is when Lee decided to go up the middle with Pickett's fresh troops as the backbone. The movie doesn't convey any of the messed up original morning plans - time constraints.

The other thing to remember in all of this, as is suggested in the film, Lee is more or less blind to what is actually happening; cavalry are your eyes and ears, as well as a screen to movement, and in this regard Lee was, firstly, surprised at finding the Union forces where he did and, secondly, unaware of the full concentration of forces at Gettysburg until too late. His strategy up until now had been, more or less, as a roaming hit and run, and that's what Longstreet was advocating here again, to withdraw and/or flank the Union army and perhaps advance on an unguarded Washington.

That Lee (in both the movie and real life) made a stand at Gettysburg is testament to both his unrelentless victories up until this point, and his opinion that the Union may not be able to withstand one more great and crushing defeat, which he thought Gettysburg had the opportunity to provide.

As with Waterloo, we have the benefit of hindsight and knowing where all the players are on the table; on the day, however, a commander is making the best use of the intelligence available at the time.

Kismet

Within the context of the book/movie and in reality, there are two different alternates about going "to he right".

General Hood mentions it shortly before going on the attack on Day 2. Hood is referring to a smaller scale flanking movement around the immediate Union right, behind the Round Tops and, ideally, into the Union army's immediate rear with perhaps a brigade or division-sized attack. Given what we now know (but which Longstreet did not know then), this might not have been the worst idea in the world, but such an attack would not have been large enough or had the support sufficient to make any lasting gains that could have changed the outcome of the battle. Longstreet would have had to put his entire corps into the maneuver in order to have had a real impact, but, even if he had been willing (and he wasn't), there was no way that he could have done it, given the time constraints, and, with the limited screening cavalry available, he could well have been attacked on his own flank if he'd tried it (Judson Kilpatrick's cavalry was, I believe, active in that part of the battlefield at that time, and Kilpatrick... as his nickname "Kill Cavalry" suggests... never saw an enemy unit he wouldn't charge into regardless of the odds).

The "way to right" Longstreet refers to in your post above is a different maneuver. Longstreet suggested throughout the campaign and, even as the battle was unfolding, that Lee should be seeking to maneuver the entire Confederate army between the Union Army and Washington, DC, finding strong ground, and then letting the Union army attack them. Lee had done the same thing in the past with smashing success (notably in the campaign leading to Second Manassas) so it would not have been an out-of-character maneuver, and, given what we know now, it might just have worked. HOWEVER, those... including Longstreet... who make the case for this movement after the fact, typically do so without a lot of the context. Lee was in enemy territory without most of his cavalry (remember Jeb Stuart had gotten himself separated from the Confederate army and only returned, with his men and horses completely exhausted and unready for any exertions at all, after the battle had begun) and with a very tenuous supply line back to Virginia should retreat eventually be necessary. Making such a maneuver without properly scouting the route (which cavalry would have done) and without proper screening to keep from being surprised by the Union army while strung out on the march (again, a job for cavalry) and with enemy civilians everywhere who would pass the word to Union troops first chance they got would have been dangerous in the extreme. Yes, it could have opened a path to win the battle... and, perhaps, the war... but it also and more likely could have opened the Confederate army up for a defeat... a defeat without a clear line of retreat that could have not just ended the campaign but resulted in the destruction of the Army of Northern Virginia and the end of the Confederacy. Even for someone as bold and aggressive as Lee, that would have been a pretty massive risk.

FYI, if you are curious about how such a maneuver might have played out, check out Newt Gingrich's alternate history novel "Gettysburg". He comes up with a semi-reasonable scenario by which Lee does perform such a maneuver and how it might have turned out.