When her previous attempts failed, Velka started the legend of the Chosen Undead that would allow her to take worthy undead warriors from the Asylum into Lordran and have them mercilessly attack and destroy the gods she's been warring with. Gwyndolin, to counter this, attempts to manipulate the Chosen Undead into his own cause, that of linking the First Flame.
It is possible that after her plots have been found out, she was banished to the Painted World of Ariamis and Gwyndolin (perhaps secretly) took over the covenant.
To support this, consider the following evidence:
Gwyndolin, leader of the Darkmoon Covenant rewards the player for killing the half human, half crow hybrids associated with the worship of Velka, found in the Painted World of Ariamis. These crows drop Souvenirs of Reprisals:
blood-drained, shrunken ears, […] taken for subduing the guilty. The knights called the Blades of the Darkmoon punish the guilt-soaked offenders of the Gods and take this as proof of their conquest. The earless corpses of the guilty will be left behind as a warning to others, inspiring both fear and respect for the Gods. Such is the eternal mandate of the Dark Sun.
This implies that Gwyndolin is using the Darkmoon Blade covenant to manipulate the Chosen Undead to kill Velka's followers.
In the same context, note that the Blades of the Darkmoon, knights of Gwyndolin, punish the offenders of the gods:
O Disciple of the Dark Sun. Thou hast journeyed far; hear my voice.
If thou shalt swear by the Covenant, to become
A shadow of Father Gwyn and Sister Gwynevere,
A blade that shall hunt the foes of our Lords;
Then I shalt protect thee, safeguarding thy person with the power of the Darkmoon.
Hunteth the enemies of the Lords, by the power of the Dark Sun.
Note how the covenant is now used to "hunt the foes of [the] Lords", instead of sinners. This might mean those who oppose the gods: Velka and her kin.
Furthermore, Gwyndolin's catalyst allows user to use sorceries with faith instead of intelligence, while Velka's Talisman enables the user to use miracles using intelligence instead of faith.
Upon the killing Gwyndolin Oswald, a pardoner of Velka has unique dialogue, seemingly congratulating the player for killing the leader of the Darkmoon Blades:
Good tidings, thou art welcome. Laudable is thy dedication to sin.
Lastly, the position of Gwyndolin being the leader of the sin-punishing covenant despite Velka being the Goddess of Sin, the following can be theorised:
Velka's two attempts failed to punish the gods, and after being possibly found out, her and her tools to punish the gods were sealed away to the Painted World of Ariamis.
It is possible that after her imprisonment (although Velka herself is not found in the Painted World in-game) a new leader was appointed to lead the covenant, but this time, to punish those who oppose to gods, slowly undoing Velka's work by getting rid of her followers.
To support this, consider the following item descriptions:
Book of the Guilty
The Goddess of Sin Velka oversees this list of the guilty, who have disrespected the Gods or their covenants, and shall one day face the wrath of the Blades of the Darkmoon.
Blue Eye Orb
These mystical orbs are granted to Blades of the Darkmoon, knights who serve the Dark Sun Gwyndolin, so that they may serve the Gods in meting out vengenance.
The Book of the Guilty is overseen by Velka, while Gwyndolin's knights seem to be serving the gods and meting out vengeange instead of punishing sinners, which can be acknowledged as a change in the purpose of the covenant, further proving the theory that Gwyndolin is using the covenant as a new leader to undo Velka's work.
The desciption of the Vow of Silence miracle of Velka seems to have been used to as a precaution against Gwyndolin, him being a magic caster himself, while other gods being known as miracle users:
Secret rite of black-haired witch Velka.
Prevents casting of magic within effect area.
Cut content reveals that there may have been a covenant devoted to Velka, tasked with hunting down Blades of the Darkmoon, which would imply that Velka and Dark Sun Gwyndolin were in fact enemies:
Ring of Condemnation
This black diamond ring is granted to those who enter a Covenant with Velka, the Goddess of Sin.
It automatically counterattacks when its wearer inflicts sustained damage.
Velka the Goddess of Sin is an eccentric witch versed in various secret rites.
Affidavit
Slip sold by bishop of Velka, Goddess of Sin.
Annul a covenant without committing sin.
A covenant is a most sacred union, normally not subject to negotiation, but when circumstances require it,
even Goddess Velka will make an exception.
