"thing" と言うと直ぐに「(ある)事」とか「(ある)物」が単純に思い浮かんでくるのですが最近読んだ次の文に出てくる "a thing" は単なる事物では無い事は推測できますね。
My mother had a thing for speed, so I was not surprised when a police car pulled us over one day as we were driving.
そこで辞書を引くと
1) A persistent illogical feeling, as a desire or an aversion; an obsession: "He has a thing about seafood."
2) an unaccountable attitude or feeling about something, as of fear or aversion: "I have a thing about spiders."
3) Be obsessed or preoccupied with something. For example, He has a thing about disorder in the garage, or Bob has a thing about brunettes.
などの説明と例が出ていました。 最初の文の母親はスピード狂なのでしょうか。