Start small. Try a new residential facility.

What is your current coping mechanism with wishes to self harm?

What about the residential facility worked? What didn't work? Are you able to find/duplicate the advantages in your current situation at home? I think this very conversation should be had with those at home.

List the things you think moving will be advantageous.
List the things that will not be an advantage (including to those you expect to move with you).
What would be your plan if it didn't work out?