You certainly have a plate full on top of your own grieving the worry about that child must be heart wrenching and I am sorry you are going through this.
The best suggestion I can offer is to try and talk your BIL into getting his son into counseling to help him process the loss of his mother and deal with his feelings. If your BIL is not responsive to doing that then ask if possible you can take him for counseling. That would benefit you both.
Rather than try and fix life for them, try and teach them or at least the child how to fix life for themselves. Make yourself available to the child when he needs to talk or discuss issues he is facing. Build a healthy relationship with him by showing him your recovery and how healthy people cope with life.
If there is a way to plead to your BIL’s heart and make going to counseling all about his child then it may be possible he would benefit along the way too. And if not at least the child will be getting professional help.
If money is an issue, schools offer counseling and you want to get some facts in order first on options before approaching them. Also check with your county they may offer some kind of free counseling as well. And of course there is always ala-teen.