I would like to know how do I get my joint custody vacated from the father.

Please define "vacated"? Are you looking to terminate the fathe'rs rights or what? Have you tried browsing the Family Law forum (where I moved this to) for similar questions?

Show that the father is some threat to the child, or that joint custody is not in best interest of the child.

Where are you located? I ask because the term "vacated" isn't used where I'm from so before I go on about the law here and find out you are somewhere else your location would be helpful.