How should I get guardianship of my nephew?

Yadda, yadda, yadda! The answer is no. You live in another state, your state will not allow him to get welfare, your insurance will not allow him on your policy, you and your mother are into pipe dreams not reality, he is a danger to your sister and his sibling, what he needs is a mental health placement not bleeding heart relatives who have no real idea of what his problems are nor the real resources to help him in any meaningful way. If there is a mental health facility designed for children in his state of residence then try to get him accepted there and help with the costs. He has a history of medication for disfunctional behavior and I am willing to bet he refuses to take his meds now which is more than half of his problem. If the best his home state has to offer is foster care that is too bad but cannot be helped. It is a tragedy but then I suspect so was his conception to a co-dependent mother and an abusive father.