Can a mentally unstable father take kids from "cheating wife"

My sisters husband was thrown out of the house about 4 months ago in that time he has tried to kill himself on multiple occasions, was diagnosed with bipolar disorder, and has threatened to kill the wife (my sister) infront of the kids, that they will "watch her die" she got a restraining order on him in the same day the threat was made. He hasnt had a job in 8 years , has nowhere to live, he is currently residing with his mother in a trailor park, he is stating that she has been cheating on him sense September of 2015 which isnt the case, does he have a chance to get sole custody of her kids. Also, the 11 year old is her son with another man from a previous relationship. Theyre daughter is 2 years of age.