His father isn't a strong presence in the household.
His father is a weak presence in the household.
「存在感」は英語で「presence」といいます。
「存在感が薄い」は「weak presence」です。
「Weak」の反意語は「strong」ですので、否定形で「not a strong presence」も「存在感が薄い」になります。
Be動詞と使ってもいいし、「have」と使っても大丈夫です。
His father has a weak presence in the household.
His father is a weak presence in the household.
彼の父親は家庭で存在感が薄い。
His father doesn't have a strong presence in the household.
His father isn't a strong presence in the household.
彼の父親は家庭で存在感が薄い。
His father does not have much of a presence in his household
彼の家庭 は his household と表現できます。
His family と言うのも有です。
父親 は 彼の父親で his father と表現してます。
父親としての責任感や意見がないのは存在感がないのに
等しいと思うのです 薄い と言うよりは存在感があまりないで
he does not have much of a presence と表現するのが
良いかもしれません。