I want him to move to the tranch, because theat would be the funniest. In reality, it is very unlikely. As insane as the tranchers are, they got a bigger hold on reality than Chris, and they won't take in a literal motherfucker after his taboobreaking went viral globally.
So, ignoring the tranch, it is interesting to consider.
Chris broke one of the biggest and most global taboo, fucking your parent. He knew what he was doing, he knew it was wrong, and he even bragged about it.
His mental retardation doesn't shield him from my moral judgement in this case because he was clearly aware.
The great unknown is Barb's condition, and if she went along with this depravity willingly or if he raped her while she was mentally unfit.
If he actually raped his elderly mother, put him in prison and throw away the key.
If not, I am not sure. Group home with lifelong community service maybe.
The asylum would be the same as prison, only that he would get drugged into oblivion, and wouldn't get "better" in any way.
Prison would be so traumatic for him that he would either shape up for the first time in his life, or it would break him.
There really is no "good" solution here, because the act is done and it was so horrific.