Boku no Tomodachi wa Mama de Asobu Tame ni Yattekuru ~**-kun Genki? Watashi, Minna ni Kakowarete Shiawase na Katei Tsukuruu~

Antisocial friends catch your (protagonist) weakness and uses it to blackmail your mother for sex.

She'll do anything for her family, but also falls to her own sexual estrum.

[From DLsite English]