Haruki hears about Kazusa's moving from her mother, who she hadn't been on good terms with.  He feels betrayed and angrily confronts her.  But his words force open the door to Kazusa's heart, which she had desperately tried to keep closed so that the three of them could stay together.
likely to be a lot of problems at home.
bedeutet, dass es zu Hause
 viele Probleme geben muss.
haber muchos problemas en casa.
por lo que podría tener problemas en casa.
elle a probablement beaucoup de problèmes 
avec son environnement familial.
que deve haver vários problemas em casa.