Using your action extends the duration on both creatures
I'm basing this answer on the way other spells behave when being split or twinned. References to a single target apply to both.
This is for Hold Person, as an example (emphasis mine):
The target must succeed on a Wisdom saving throw or be paralyzed for the duration. At the end of each of its turns, the target can make another Wisdom saving throw. On a success, the spell ends on the target.
With the spell twinned, now target refers to both creatures. I see no reason for the action to continue the spell to not apply to both as well.
Furthermore, here's a tweet by Mike Mearls in response to a similar question:
One spell instance, two targets.
That tells me, the Split spell continues to act as close as it did before but with the added second target. You are not concentrating on two spells, and you don't need to spend an action on each creature; one action works for both.
See Witch Bolt for a similar case (PHB, p. 289; emphasis mine):
On a hit, the target takes 1d12 lightning damage, and on each of your turns for the duration, you can use your action to deal 1d12 lightning damage to the target automatically.
If twinned, your action lets you damage both the new targets. The wording is a bit different but wording of spells isn't always 100% consistent from what I've seen. I think it's very likely Crown of Madness is intended to work the same way.
As for the other questions:
- If just one action is sufficient to maintain control of both targets, can the caster elect to end control of one target but not the other?
No, you can't. If we treat it like any other spell with multiple targets (say, for example, an upcast Hold Person), by RAW, you can drop concentration at will, ending the whole spell, but there's nothing that lets you end only part of the spell.
- If the spell ends on a single target (either by choice or through lack of a required second action), does the spell automatically end on the second target? (because of the 'or the spell ends' clause)
This requires some development.
First, I think you were asking mainly in the case that you couldn't keep both crowns with one action, or if you could choose to make one stop at will while keeping the other. Since neither of those is the case, that part of the question becomes redundant.
However, I think there is still a case where it's worthwhile to consider what happens. It's quite a common situation, actually, because that situation is, what happens when one of the targets makes the save?
If we compare the wording of Hold Person above to Crown of Madness (PHB, p. 229; emphasis mine):
Also, the target can make a Wisdom saving throw at the end of each of its turns. On a success, the spell ends.
It would seem there's a difference in the way the spells stop. A creature passing the saving throw of Hold Person ends it on itself, while a creature saving for Crown of Madness ends the whole spell. That would be in line with this answer to a similar question.
Now, my contention with this is that single-target spells aren't written to reflect their behavior when applied to multiple targets. Even Hold Person speaks about a single target (emphasis mine):
Choose a humanoid that you can see within range. The target must succeed on a Wisdom saving throw or be paralyzed for the duration. At the end of each of its turns, the target can make another Wisdom saving throw. On a success, the spell ends on the target.
When it should read something like (emphasis mine):
Choose a humanoid that you can see within range. Any target must succeed on a Wisdom saving throw or be paralyzed for the duration. At the end of each of their turns, each target can make another Wisdom saving throw. On a success, the spell ends on the target.
So, the difference between Hold Person's stopping condition and Crown of Madness' can be chalked up to the fact that Hold Person can be upcast to affect multiple creatures, so that situation was taken into account for a very in-game relevant aspect of the spell. But the rest of the wording of the spell is left simple to fit the single target use of the spell.
Answering the question: By RAW... maybe?.
My position is that RAW is not written for multicasting these single target spells, so modifications should be made to make the spells make sense. I think it's reasonable to modify the stopping clause of the spell as well to make it more like Hold Person's. Now, someone could take the stance that only the minimum number of modifications should be made for the spell to make sense and still abide by RAW as much as possible and the stopping clause doesn't need to be changed to work in a multicasting scenario. And that is a reasonable stance too.
Still, by my interpretation of the rules, definitely.
- How might the spell be reworded to demonstrate the RAW effects on two targets?
Replacing each instance of "target" with "each target" might work, "any target" may be even clearer.
I would also replace: "On a success, the spell ends" with "On a success, the spell ends, for that target".
Note that this doesn't make the spell particularly clearer for a normal reader without a multicast feature, which is likely be the reason why the spells aren't written that way to begin with.