According to Apollonius Rhodius' Argonautica 2.966ff, Heracles, while performing his ninth task, which required him to obtain Hippolyta's girdle, captured "Melanippe, daughter of Ares," and as a trade, "Hippolyte gave him her glistening girdle as her sister's ransom," whereupon Heracles let Melanippe go free, unharmed.
The Amazon leader with whom Antiope is usually confused, or identified, is Hippolyta. Writing a couple of centuries after Apollonius' time, Diodorus Siculus, in the Library of History 4.28.1 explains the reason that the Amazons attacked Athens during the reign of King Theseus: "They were especially eager to punish the Athenians because Theseus had made a slave of Antiope, the leader of the Amazons, or, as others write, of Hippolyta."
Diodorus clouds the issue over a little bit further in his narration of Heracles' ninth task earlier on in 4.16, at the beginning of which he tells us that "Heracles then received a command to bring back the girdle of Hippolyta the Amazon and so made the expedition against the Amazons." At the end of the chapter, 4.16.3-4:
The commander of the Amazons, Melanippe, who was also greatly admired
for her manly courage, now lost her supremacy. And Heracles, after...
killing the most renowned of the Amazons and forcing the remaining
multitude to turn in flight, cut down the greater number of them... As
for the captives, he gave Antiope as a gift to Theseus and set
Melanippe free, accepting her girdle as her ransom.
This is a little bit bewildering, since Diodorus, after the beginning of the chapter, where he has told us that the famous girdle belongs to "Hippolyta the Amazon", never mentions Hippolyta again. And now at the end he seems (suddenly?) to be saying that the girdle belongs to Melanippe, "the commander of the Amazons," who, it seems, contrary to Apollonius Rhodius' account, uses this prize to ransom herself rather than anyone else.
Perhaps another way to interpret the sentence could be that the "her" here refers all the way back to Hippolyta at the chapter's beginning, so that Theseus receives Antiope as a prize while Hippolyta uses her girdle to ransom Melanippe. It's either that or we'd have to assume that Diodorus understands Melanippe to be another name for Hippolyta. He otherwise never says anything about the familial relationship, if any, between Hippolyta, Antiope and Melanippe, nor does he mention any genetic connection between them and Ares.
The History of the World, the work of Pompeius Trogus, a Gaulish contemporary of Diodorus Siculus, survives in the Epitome which a Latin historian named Justin made of it. According to this Epitome, when Hercules [Heracles] came to the land of the Amazons, they were ruled over by two sisters: Antiope and Orithyia, who themselves had two other sisters, namely Menalippe and Hippolyta.
Menalippe, whose name has got to be a mangled form of Melanippe, having been captured by Hercules, was ransomed by Antiope, who gave to the invader her arms rather than her girdle. (Hercules' mission in this version is to capture arms; no mention of a girdle is made.) Hippolyta is the Amazon whom Theseus makes his wife in this rendition of the story.
Orithyia is said to be the daughter of a previous queen named Marpesia. Presumably the other sisters are also Marpesia's daughters. The Epitome implies that the idea that the Amazons are daughters of the war-god is based merely on a report spread about by Marpesia and her co-queen Lampedo. The History of the World Epitome says that:
After Orithya, Penthesilea occupied the throne, of whose valour there
were seen great proofs among the bravest heroes in the Trojan War,
when she led an auxiliary force thither against the Greeks.
We are never told here in what way Penthesilea might be related to the previous queens, assuming she is supposed to be.