Long time ago i had a cat like this. He would come to the door, visibly happy to see me, but no touchy.
Never … When picking him up, he melted away. When trying to touch him, he was like when you try to bring two magnets together using the same poles.
But he was always right next to me.
Glad you escaped and i hope you two find a new home quick.
Abusive family members are hard to deal with.