As pointed out by @Adamant in the comments, this is most likely the Tunnels series by Roderick Gordon (started in 2007, six books total).
Summary of the first one, from Goodreads:
14-year-old Will Burrows has little in common with his strange, dysfunctional family. In fact, the only bond he shares with his eccentric father is a passion for archaeological excavation. So when his dad mysteriously vanishes, Will is compelled to dig up the truth behind his disappearance. He unearths the unbelievable: a subterranean society that time forgot. "The Colony" has existed unchanged for a century, but it's no benign time capsule of a bygone era. Because the Colony is ruled by a merciless overclass, the Styx. Will must free his father--is he also about to ignite a revolution?
TVTropes confirms the eggs part, as well as the Earth being a ship:
Bizarre Alien Reproduction: The Styx appear to reproduce like their hosts for the most part—they can even interbreed with the host species, because, just like Xenomorphs, they use the host's DNA to modify their own appearances to look just like them. During the phase the females instead produce eggs on their own and implant them into hosts from other species, creating warrior caste Styx. They can also produce Armagi, which are all male, but also multiply by planting eggs in a similar way. [...]
Planet Spaceship: Earth itself turns out to be one at the conclusion of Terminal.
