L.S.
If she is despessed, drinks heavy and has problem why on earth would she or her husband want to bring another child into the world. Sorry I know that sounds mean but it's reality. Why would you help? I think what you should do is make yourself "busy" and not contribute to her behavior. Her behavior is rubbing off on her son. Do you really need help from her? That is the only thing that would keep me in her life. I would try talking to her one on one if this is the case by yourself only adults. You have enough on your plate with three little one, I don't think you need any more.
If you continue watching her son I would tell her that she has to tell you in advance and if she keeps canceling tell her you just can't do it any more.
On a side note no parent likes to hear about their child being a "bad" child. When you take care of him just tell her what he did don't offer any comments. But if it continues tell her that your children's saftey come first and you aren't going to be able to watch him if he's means and hurtful.
It will rub off on your child as well.
Be safe with your children.
L.