C (the succubus) can't directly attack A (the eladrin), but C's previous command to B still stands
The charmed condition on its own is pretty limited in what it does:
- A charmed creature can't attack the charmer or target the charmer
with harmful abilities or magical effects.
- The charmer has advantage on any ability check to interact socially
with the creature.
The succubus' Charm action is more specific (emphasis mine):
Charm. One humanoid the fiend can see within 30 feet of it must succeed on a DC 15 Wisdom saving throw or be magically charmed for 1 day. The charmed target obeys the fiend's verbal or telepathic commands. If the target suffers any harm or receives a suicidal command, it can repeat the saving throw, ending the effect on a success. If the target successfully saves against the effect, or if the effect on it ends, the target is immune to this fiend's Charm for the next 24 hours.
The fiend can have only one target charmed at a time. If it charms another, the effect on the previous target ends.
If a succubus charms a creature and it fails the Wisdom save, it must obey the succubus's verbal or telepathic commands. The only exceptions are if it suffers any direct harm or receives a suicidal command (such as to throw itself into lava), in which case it can repeat the save. If the succubus commands a charmed target to attack an ally, the charmed target follows that order.
The succubus (C) can Charm B, and then (assuming B fails the save) command B to attack A. So far, so good.
Then, we look at the eladrin's Fey Step feature (MToF, p. 62):
As a bonus action, you can magically teleport up to 30 feet to an unoccupied space you can see. Once you use this trait, you can’t do so again until you finish a short or long rest.
When you reach 3rd level, your Fey Step gains an additional effect based on your season; if the effect requires a saving throw, the DC equals 8 + your proficiency bonus + your Charisma modifier:
Autumn. Immediately after you use your Fey Step, up to two creatures of your choice that you can see within 10 feet of you must succeed on a Wisdom saving throw or be charmed by you for 1 minute, or until you or your companions deal any damage to it.
Unlike the succubus, the autumn eladrin's Fey Step simply imposes the charmed condition on a failed save, with no additional effects. Nothing about the condition forces the charmed target to obey the eladrin's orders in general. The charmed target simply can't harm the eladrin directly, and the eladrin has advantage on social interaction checks against the charmed target (e.g. Persuasion, Intimidation, Deception, or other Charisma checks not associated with specific skills).
The eladrin (A) can use Fey Step to teleport within 10 feet of the succubus (C), then attempt to charm it; if the succubus fails the save, then it is charmed by the eladrin. This prevents the succubus from directly attacking the eladrin.
However, nothing about this situation on its own affects the succubus' previous command to B, who is still charmed by the succubus - so if nothing else is done, B will still attack A (the eladrin) on A's turn. A could attempt to convince C (the succubus) to tell B to stop attacking, but there is no guarantee of success.
As C is an enemy monster, A's Charisma check (at advantage) would be made against a fixed DC; given that the two sides were previously in combat, it would likely still be quite difficult to convince the succubus to call off the attack.
Of course, the DM might decide that the charmed condition does provide some magical encouragement for the charmed target to find the charmer's demands more appealing, and so they might decide to set a less extreme DC for the check. In other words, it might be normally impossible to convince an enemy that's actively fighting you of something, but the charmed condition, in principle, makes them treat you as less of an active enemy - at the least, they can't attack you directly, and they're receptive to what you have to say - so that might make it possible (even if still difficult) to convince them of that thing.