Rena's mother worked as a designer at a small clothing factory in Okinomiya, where she met and married Mr. Ryūgū. They started out in a cramped apartment before moving into his mother's house once Rena was born, where they stayed until Rena began elementary school.
When the factory hit financial trouble, Rena's mother saw an opportunity to go independent with some colleagues. Instead, she landed a better offer from a design firm in Ibaraki with serious projects lined up—they clearly believed in her talent. The family relocated, but Mr. Ryūgū had to leave his job and become a stay-at-home parent. He struggled with it. He couldn't cook, kept bouncing between odd jobs at small companies, and generally wasn't cut out for housework. Rena ended up doing most of the chores herself while still a kid.
Things got dark from there. Rena's mother sent lawyers to the house repeatedly but refused any direct contact—no visits, no phone calls. Both Rena and her father fell into depression. They saw her one more time, but she wouldn't even read the letter Mr. Ryūgū had given Rena to pass along. That was the last meeting they ever had.
In the Tsumihoroboshi arc, Mr. Ryūgū gets tangled up with Mamiya Rina, who manages a club called Blue Mermaid back in Okinomiya. She and her associate Hōjō Teppei run a con on him—she fakes a pregnancy to push him toward marriage. Before the trap can fully spring, Rena kills her. Teppei attacks Mr. Ryūgū anyway later that night, and Rena kills him too.
The Minagoroshi arc plays out differently. Rena actually talks to her father about the situation instead of acting alone, and he manages to land steady work that time around.
Content compiled by AnimeList.moe from publicly available sources.