My mom kicked me out but is now threatening and continuously harassing to have me arrested as a runaway if I don't stay with my dad. However my father is giving me permission to stay with a friends family throughout the summer. He needs FULL custody of me so she'll stop harassing me. What do I do?

So your dad takes your mom to court to bet custody, using mom throwing you out as proof.

YOU do nothing. Your dad goes to court for a modification of the custody order. If mom is in agreement should be a slam dunk.

Let your parents handle it.

If your mom reports you as a runaway and then you or your dad explain the situation, it may backfire on her.

Be sure your dad has given the people you are staying with some sort of written permission as well as a medical release to in case of emergency.

Good luck

Of course if dad does nothing, mom reports you as run away, police arrest you, they put you in Juv detention where you sit till a court hearing ( unless your mom takes you back in to her house since she is the one with legal custody)

If your dad does come to court to testify about the run away, the judge may not even believe him, since in family court ex husband and wife lying about each other is normal

Dad can not and does not have the legal status to give you permission to do anything.

Safest bet would be to live with him, and he file for custody