I don't actually think he is at his moms. It's weird how everyone visits him, he does not go to them. They also always meet him at the same table, like that is where people meet. The schedule he is on and the fact that he eats with the same person everyday makes it seem like he is in a hospital of some sort. Maybe a psych ward. I think a lot of this is happening in his head. The way Ray was able to get him out of the hospital so easily after the beating is probably because he runs the hospital and/or psych ward.
No one ever says that Elliot is with his mother.