She used to interject her own thoughts when other people were talking to her.
この場合、次のように言えます。
ーShe used to interject her own thoughts when other people were talking to her.
「彼女は人が話しているとよく自分の意見をさしはさんだものだった」
to interject one's own thoughts で「自分の考えを話し半ばに差し挟む」
ご参考まで！
"She would always interject when people were talking."
"She always interjected as soon as someone started talking."
"She would always interject when people were talking."
"she would always ~" 「彼女はいつも〜」
"interject" 「言葉を差し挟んだ」代わりに "interrupt / interrupted" もつかえます。
"when people were talking" 「人が話をしてると」
"She always interjected as soon as someone started talking."
"as soon as" 「すぐに」
"someone started talking" 「人が話して始めると」
カナダ 
オーストラリア 
