Hitters 1 and 2 bat in the first inning in reverse order, neither reaches base

In the 3rd inning, they bat in reverse order again (2 then 1). One of them reaches base, coach appeals.

Are they still out of order? Or did they establish a new batting order?

They are still out of order.

I believe that they established a new batting order in the first inning (technically, I think they established two new batting orders! ---but the last one would supersede the first). It was too late to appeal in the third inning.

OBR 6.07
BATTING OUT OF TURN
(a) A batter shall be called out, on appeal, when he fails to bat in his proper turn, and another batter completes a time at bat in his place. (1) The proper batter may take his place in the batter's box at any time before the improper batter becomes a runner or is put out, and any balls and strikes shall be counted in the proper batter's time at bat. (b) When an improper batter becomes a runner or is put out, and the defensive team appeals to the umpire before the first pitch to the next batter of either team, or before any play or attempted play, the umpire shall (1) declare the proper batter out; and (2) nullify any advance or score made because of a ball batted by the improper batter or because of the improper batter's advance to first base on a hit, an error, a base on balls, a hit batter or otherwise....(c) When an improper batter becomes a runner or is put out, and a pitch is made to the next batter of either team before an appeal is made, the improper batter thereby becomes the proper batter, and the results of his time at bat become legal. (d)...(2) When an improper batter becomes a proper batter because no appeal is made before the next pitch, the next batter shall be the batter whose name follows that of such legalized improper batter. The instant an improper batter's actions are legalized, the batting order picks up with the name following that of the legalized improper batter. ...If an improper batter bats and reaches base or is out and no appeal is made before a pitch to the next batter, or before any play or attempted play, that improper batter is considered to have batted in proper turn and establishes the order that is to follow.

The batter order can never change, the fact the batters hit out of order the first time does not effect the order the next time through, the batting order is that which is given to the Home plate umpire and or official score book.

See C above, when an improper batter is legalized because of a pitch to the next batter then the batting order simply picks up from the now legalized batter. In the original example this was great coaching by the defense, let em hit out of order as long as it doesn't hurt us, but rather hold on for later on in case it will. I had to hog tie and tackle one of my assistant coaches for this type scenario, when the big home run hitter on the other team came up out of order with the bases juiced he (my coach paniced and tried to go screaming to the ump, I gagged him and let the guy swing away, no win situation for them, he popped out but we were still ready if he'd come up again.