I was a bit on the fence regarding this, but this part cinched it for me:
いつもおどおどと姉や母に振り回されている父だが、今日は堂々とした態度だった。
And this bit made me sure of my suspicion that Yuu’s mother might be parentifying him:
由宇はまるで夫のように、おばさんの背中を撫でていた。
I agree with @Scylie about the ethics of dragging Yuu into this. But I wonder if this might be not just about staking a claim to her own body, but also about experiencing sex in a safe environment, as a ‘trial run’ for what she knows she’ll be forced to endure later?