not that i heard of. i can't think why anyone would want to conquer the underworld, its grim down there. well, i suppose there's a lot of wealth in the ground come to think of it. on the other hand its easy to imagine that Hades might want some land in the sun. So i can see why he might invade up here.
There wasn't much Zeus vs. Hades myth that I've ever heard of. There were times when they had differing opinions (concerning souls and deaths of some of Zeus' sons), but according to Homer and Virgil, and also Powell I believe, Hades rarely left the underworld. I can't remember which said so, but according to one poet, Hades was never seen out of the Underworld; even during the abduction of Persephone. Apparently, in that specific myth, there was no thundering black chariot pulled by giant black stallions, he simply opened the earth so that she fell through the ground and into the Underworld...and we know what happened from there. Hades was the god of, not just the underworld, but wealth, he would have had everything (except sunshine). According to Edith Hamilton, Hades felt alone because he was surrounded by his souls, but had no companion, so he stole Persephone and did all he could to please her. When she finally fell in love with him he was pleased and, as far as I can tell, he was happy from then on and pretty content in his realm. I think that, like with Apollo and the sun-chariot, Zeus would have been lost trying to rule the underworld and Hades would have been lost trying to rule the heavens.
There is only one story in the original Greek mythology in which Zeus ever entered into a conflict with Haides (Hades). When Zeus' son Herakles (Hercules) went to war against the city of Pylos in Messenia, which was ruled by his cousin Neleus, some of the gods joined the conflict and took sides, similarly to the manner in which they did the same thing during the great war at Troy a generation later. At this time, Hera, who hated her stepson Herakles; Poseidon, coming to the aid of his son Neleus; and Ares, who had locked horns with Herakles before (and would do so again), all came to the aid of Pylos, to which Herakles was laying siege. Haides also threw his lot in with the Pylians, because he was worshipped in their city, and this would seem to be a unique occurrence in Greek religion, since Haides had a very limited cult, most Greeks traditionally being afraid to even to call him by his real name. Seeing this state of affairs, Herakles' father Zeus and half-sister Athena came to his aid and together they defeated their opponents. Herakles, though, was the star of the show. He himself killed Neleus and almost all of his sons and single-handedly wounded each of the gods who opposed him, with the exception of Poseidon. Having been so brutally dealt with by the hero, Hera, Ares and Haides each had to repair to Olympos to seek healing from the gods' doctor Paion (a form of Apollon) up there. So in the story, the conflict directly between the gods seems to be minimal, Hiades' involvement in it being mainly to support Pylos against Herakles' onslaught. Other than that, Haides, in the mythology, is invariably a supporter of Zeus, who always treats him in a friendly manner. There are two occasions in which this is most obvious. In one, it was Zeus who originally organised for his own daughter Korē to be abducted by her uncle Haides, after which she became Persephone, the queen of the Underworld. In the other, when Haides complained to Zeus that Asklepios (Asclepius) was greatly depopulating the Underworld by resurrecting so many of the dead, just as he was on the point of resurrecting the giant Orion at the request of the goddess Artemis, Zeus blasted Asklepios dead with a thunderbolt. The modern stories in movies, novels and comicbooks in which Haides is constantly at odds with Zeus mostly depict Haides as an evil, Satan-like being, and his domain, the Underworld, as a sort of version of the medieval European conception of Hell or the Lake of Fire from the Bible. But the ancient Greeks did not conceive of Haides or the home of the dead as necessarily evil or "Hellish." Even Tartaros, the storm-wracked pit or abyss in which the souls of the damned were tortured for their sins in life, was thought of as such a place only later in Greek history, and even then it was only a part of the Underworld, not the whole show. The main "evil" of the Underworld and its king was that it was as drab, dreary and inglorious as possible a version of the life a human being experienced while alive. But it was not necessarily suffering. The god Haides was only thought of as cruel in that he was the lord of the dead, and when the time came for him to collect, he, as a representation of death, was merciless and generally impartial. But even the Greeks generally accepted that death was an evil which made up a part of life. If anything, there are more references in Greek mythology to Zeus being cruel, merciless and downright evil than there are any describing Haides in this manner. But on the other hand, Haides and Zeus were apparently so similar that it didn't seem strange to refer to Haides as Zeus Khthonios or Katakhthonios, the "Earthly/Infernal Zeus," or the Zeus of the Underworld, who was depicted enthroned, like the sky-god, wielding an eagle-tipped sceptre. Zeus himself was sometimes depicted enthroned with Kerberos (Cerberus), the monster watchdog of the Underworld, sitting next to the god's throne, as though there were really no difference between Zeus and Haides. Ironically, the one brother of Zeus of whom there is a story of his [once] having tried to overthrow Zeus, i.e., Poseidon, seems to be invariably depicted in modern media as his friend and ally. Poseidon once actually spent a whole year, together with his nephew, Zeus' son Apollon, labouring as slaves of mortals on account of their having attempted to overthrow their king Zeus.
