DC Comics does not own Hippolyta. Obviously, the version that gives birth to Wonder Woman is safely owned by DC, but the character of Hippolyta is far too old for any company to definitively own. After all, Hippolyta is one of the Amazons, a society first conceived of in Greek and Roman folklore and myth. Hippolyta is a part of Hercules and Theseus's hero journeys. DC brought Hippolyta into Themyscira to bring to life to one of its greatest heroes, but Marvel took a very different approach. In fact, her journey crossed over with a very different God: Thor.
While Hippolyta is a hero in DC, Hippolyta in Marvel is an agent of Death, first serving Pluto before joining with Hela. It all began in the pages of Stan Lee and Jack Kirby's run on Thor.
Hercules
In the Roman myths from which Marvel and DC draw heavily, Hercules is not exactly as heroic as his Disney counterpart. He steals Hippolyta's magical girdle and assaults her. In the Marvel Comics iteration of the myth, the two meet when Hercules, Jason and the Argonauts all invade Themyscira but, despite some resentment over the whole invasion deal, the two actually engage in consensual sex. Hippolyta tries to forge a lasting relationship, but Hercules breaks it off and repeatedly turns down Hippolyta's offers. This leads Hippolyta to ultimately resent Hercules.
From here, Marvel further diverges from both the Roman mythology and DC's version of Hippolyta. Marvel's Hippolyta is ultimately killed by her sister shortly following the Trojan War, so she goes to the underworld. While she lingers there, she'ss eventually contacted by Pluto to take part in an elaborate scheme to trap Hercules. Hippolyta agrees, eagerly. She poses as a movie starlet who enters into a relationship with Hercules and writes up a "movie contract" -- which is actually a seal that traps Hercules in the underworld -- which he signs without reading.
He would remain trapped forever if not for Thor, who goes to the underworld to help Hercules break everything. They prove to be such a pain in Pluto's butt that the God of the Dead voids the contract just so they both leave.
Pluto and Hela
Pluto later brings Hippolyta back to life again and contracts her to marry Hercules as part of another elaborate scheme to conquer Olympus. This scheme results in the formation of the Champions of Los Angeles, a superhero team consisting of Hercules, Ghost Rider, Black Widow, Iceman and Angel. The Champions prevent Pluto's conquest, which leaves Hippolyta now on the radar of other superheroes.
Still an agent of Pluto, Hippolyta starts recruiting female runaways from New York City to recreate her Amazon legions, which results in the formation of the Bacchae, a team of adversaries who are eventually defeated by the Fantastic Four and X-Men. However, after orchestrating another elaborate scheme to bring Hercules back to her, Hippolyta's daughter, Artume, kills her again.
This is where Hela, the Goddess of Death, enters the picture. Hela brings Hippolyta back to life to serve her, granting her the code-name Warrior Woman -- a name remarkably similar to Wonder Woman, especially considering her DC counterpart. Hela uses her to combat the Doom Maidens alongside Valkyrior before the pair join the Fearless Defenders. All of this, however, would have been impossible had Thor not defeated her back when she first tried to lock Hercules in the bowels of the underworld.