Controversial but YTA. Put yourself in your sister’s shoes. How desperate would you feel if you were dying and knew your kids would go to the foster system? You are his family, if you don’t want him, can you imagine how he will be treated by complete strangers? Of course, it would be an immense sacrifice by your entire family, but like I said, he is also your family. I cannot imagine turning my back on the people I love, and I am sorry but in my opinion that’s what you will be doing.

In the very least you should try to make it work. Take Alan in, get professional help, set rules for interacting with your other kids, ask for advice in subreddits, whatever. Just try for his sake. He is a child, he is not to blame for being a handful, maybe in a few years you could all sort it out and have a bigger, beautiful family. Alan must be going through a lot with his condition and mother in the hospital, literally cut him some slack.