The babies are born when MC and company (there're two side pairings) are at robot exhibition and getting attacked by people from higher civilization (other planet). 3 eggs hatched there, but 1 egg is kidnapped by the bad guy.
It should be a happy event, but since the situation is like that, they're more worried about the kidnapped egg. After this, the setting of the story moves to the higher civilization planet.
IMHO, the later story isn't as cute as the beginning since it's more about MC and ML repopulating the planet via pregnancy drug (male & female who take it will get pregnant through sex or even sperm cell injection, the amount of baby depends on how many pill they take) and rooting out the bad guys.