To start with, I have never watched a movie with this kind of a plot. But since, you've given a very long and detailed description, overcome by curiosity, I googled for the movie title. After some long browsing, I realized that what you are describing is not a movie at all, but a video game. This plot you've mentioned is exactly similar to the plot of the 1998 game Battlezone. Here is a link to the wikipedia page of the game from where you could read the entire plot of the game. But for your reference, here is the beginning of the game plot.
Battlezone is set during the 1960s with an alternative history plot, in which the Space Race is used to cover up the deployment of the United States and Soviet militaries into space. Both sides have used scraps of extraterrestrial "bio-metal", which have fallen to Earth as meteors, to build vehicles with amazing properties such as hover capability. Both nations deploy into space and are fighting across the solar system to control other deposits of the bio-metal. Gameplay is divided up into two campaigns; one following the American National Space Defense Force (NSDF), the other with the Soviet Cosmos Colonist Army (CCA, also referred to as the Communist Cosmonaut Army in early game manuals).
The American campaign starts on the Moon, but the NSDF is forced off after the destruction of their main base. They relocate to Mars, but find the Soviets already there. Both sides locate alien artifacts, and the Americans also find a factory; the long-dead alien race that created the bio-metal is identified as the Cthonians, who inhabited the planet Icarus (now the asteroid belt) and visited Earth on several occasions, influencing Greek mythology. The Americans learn of an ultimate weapon called the "Fury" and head to Venus to learn more about it. 99
Another Cthonian relic is recovered, pointing to Jupiter's moon Io. The NSDF finds a third relic, but this is stolen by a scientist defecting to the Soviets. The player must steal a Soviet fighter craft and tap into the communications network, which reveals the CCA relocation to their main base on Saturn's moon Titan. The Americans clear nearby Europa of CCA units to prevent early warning to those on Titan, but the main assault is annihilated, as the Soviets have begun to manufacture Fury vehicles. However, the Furies turn on the Soviets; they are self-aware and programmed to destroy all life. Icarus was destroyed by the Cthonians to prevent the Furies from reaching Earth. The NSDF and CCA ally against the new threat, and after destroying the production factory on Titan, travel to the fictional moon of Achilles, orbiting Uranus. The Americans destroy the main Fury base, but this causes the moon's core to destabilise, and the player must destroy the Furies' evacuation vessel before it escapes, then escape themselves.
You can read the rest of the plot from the wikipedia page to which I gave the link above. The plot, including the names of the moons and races is just as you described. The only difference I noted was that the name of the ultimate weapon is changed to Fury in the game whereas you mentioned it to be Chimera.
It's amazing that you could remember such a vivid amount of details, including the names of races and weapons and yet not recall it to be a game. Could it be that you read the description from somewhere or watched someone play the game and you later remembering only the content, led to believe that it was a movie? Now, I'm sorry if there is a movie with the same plot, made from the game or vice versa, but I however was not able to find any after an extensive google search. Hopefully, this answers your question. 963