What Big Teeth by Rose Szabo.
Eleanor Zarrin has been estranged from her wild family for years. When she flees boarding school after a horrifying incident, she goes to the only place she thinks is safe: the home she left behind. But when she gets there, she struggles to fit in with her monstrous relatives, who prowl the woods around the family estate and read fortunes in the guts of birds.
Eleanor finds herself desperately trying to hold the family together — in order to save them all, Eleanor must learn to embrace her family of monsters and tame the darkness inside her.
Eleanor's mother is, as you say, half covered in polyps:
“Eleanor,” Grandma Persephone said. I was already looking past her, looking for the voice that had called to me earlier. But when I really saw my mother, I gasped.
She was wearing a thin robe, drenched with water. Half of her face was just like mine. I recognized my high forehead, my profile. But as she turned to look at me I saw her other side: an eyeless, earless mass of red polyps that ran all the way down her body until they disappeared into the water of the tub. All of them were straining toward me, as though they could see me, as though they wanted to reach out and grasp me and suck me into the mass. I stumbled back and caught myself on the porch railing.
Eleanor's sister is Luma, not Luna, and the cousin is Rhys. He is accidentally eaten by Eleanor and left in a coma:
Scattering crows in his wake, Rhys lunged at her. “Stop!” I yelled, but it was too late. His momentum carried him forward even as he turned to try to obey me. Grandmere lashed out a tentacle, snatched him up, and flung him toward the maw.
Without thinking, I opened my mouth and breathed in.
He hung, for a moment, suspended between us. And then Grandmere let go, and Rhys was flung backward. Before I knew what had happened, he disappeared.
I yelped and spat him back out. He lay on the floor unmoving. I was still rooted to the spot; I couldn’t run to him. I couldn’t tell if he was still Rhys, or a thing.
There is no butler in the story, but it does end with Eleanor fighting her grandmother and the house is set on fire by a mob from the nearby town and burns down while they are fighting.