Chikyuu Bouei Kazoku OVA

The Daichis are a family in danger of tearing itself apart. Dissatisfied and money obsessed mom Seiko has served wimpy and otaku dad Mamoru with divorce papers. Daughter Nozomi who has always been saddled with all the housework, feels pained that everyone is using her. The youngest albeit most foul mouthed, Dai is forced to watch all this as everything is going to pieces. However when the Galaxy Federation recruits the Daichis to combat alien threats to the wellbeing of the Earth, it will be a chance for the family to save the world and maybe themselves.

(Source: Anime News Network)

Note: Was originally planned to be released as episode 11 of the TV series but a replacement episode was made and this was later released on DVD.