She became hysterical around that time and vented her frustration on her family.
She got a little crazy around that time and took it out on her family.
いろいろな言い方がありますが、次のような表現を覚えておくと良いと思います。
ーShe became hysterical around that time and vented all her frustration on her family.」「その頃、彼女はとてもヒステリックになり、家族に当たり散らした」
to vent one's frustration on one's family で「家族に当たり散らす」と言えます。
ーShe got a little crazy around that time and took it out on her family.
「その頃、彼女は気が変になっていて、家族に当たり散らしていた」
to take it out on one's family でも「当たり散らす」と言えます。
ーShe was spiteful towards her family.
「彼女は家族に当たり散らした」
spiteful「悪意に満ちた・毒々しい」を使っても表現できます。
ご参考まで！
カナダ 
