First, my partial solution to the problem of Antony's yo-yo emotions in the second half: booze. It's a bit of a cheat, but several characters in Act One do reprove Antony for partying too much in Egypt; and he himself admits at one point that he neglected important duties because he was too hung over. When he rushes back to Cleopatra, it makes sense that he would also be rushing back to Egyptian wine...and that would lead to a loss of emotional control, and eventually to bad choices, like we see in both of the battles.
John has no problem adopting this approach, and it's easy as pie to work it in -- we just make sure Antony has a goblet in his hand as often as possible. But it does change one thing -- namely, Antony's degree of blamefulness increases dramatically. His accusations to Cleopatra become cheap attempts to displace the blame that he clearly deserves for these significant screw-ups. When he flees from the battle at Actium (after watching Cleopatra retreat), he says
My heart was to your rudder tied by th’ strings,
To tow me after.
And, since Cleopatra is crying "Pardon!" it's easy for us to forget that Antony is the military general, not Cleo. Similarly, in the second battle, when he briefly perceives that he might be gaining the advantage, Eros points out that the Egyptian reinforcements have not embarked. Why not?
EROS: You never gave the order, sir, to launch.
Nevertheless, Antony blames Cleopatra -- accuses her of "packing cards with Caesar," even. This sort of loose, desperate blame-calling isn't Antony's style; but then, as he keeps reminding us, Antony is "not himself" anymore. He has drunk himself into oblivion.
An intelligent alcoholic knows they are at fault. Antony says "Betrayed I am," and the line refers to Cleopatra -- but inside, he knows better. And here's where things get tricky, and the line readings begin to bend around backwards, to the point where they're nearly 180 degrees.
Cleopatra re-enters, and Antony curses her with words he knows will drive her away:
Vanish, or I shall give you your deserving
And blemish Caesar’s triumph. Let him take you
And hoist you up to the shouting plebians!
Follow his chariot like the greatest stain
Of all your sex; most monster-like be shown
For poor diminutives, for dolts, and let
Paitent Octavia plough your visage up
With her sharp nails! You’ll die for this!
On the surface, these lines mean exactly what they sound like. But, if Antony knows that she's not deserving of any such fate -- if he knows that he is to blame for their downfall -- then the intention changes. Now, he wants to minimize any further harm to Cleopatra. His alcoholic's mindset says "I'm cursed, I'm useless, I'm a bad egg. Anyone who sticks with me will sink along with me." And therefore, Antony's intention is to drive Cleopatra from him so that she might retain a fighting chance of surviving Caesar's invasion.
Antony carries this intention into the next scene, and when Mardias enters, he curses Cleopatra thus:
ANTONY: She has betrayed me and shall die the death!
Subtext: keep her away from me, or she'll get hurt. But Cleopatra, who misinterpreted his rage, sends Mardias after him to tell him she has slain herself. Jennifer (who plays Mardias) long ago established that she disapproves of Cleopatra's emotional games, and this is the worst game by far. But she does her job, and shows up to inform Antony that
Death of one person can be paid but once,
And that she has discharged. The last she spoke
When we ran it tonight, I told Jennifer to play against the line. Her job is to tell Antony that Cleopatra is dead; but her intention is to convey the opposite information: this is a ruse, this is a game, Cleopatra needs you, go to her.
Antony, however, misses the subtext. Suicides ensue. And there you have it: two desperate characters, saying the opposite of what they ought to be saying. Will the audience penetrate all that subtext? Ah, who cares. Either way, it's a stirring scene. And there are swords. How can you go wrong?