My cousin has agreed to let her teenager live with me, how do I get temporary custody

A notarized document signed by her giving you permission to act on her behalf will work for many things. Many schools will allow this and often times so will a doctor. However, only a court order can grant custody. So it may not work for all of the things you want to accomplish. Remember also that she can revoke this at any time. If she does this then the child will have to go back with her. Also where is the father, if there is a court case then the father may have to be served. Good luck and have a great 2015.

For the purposes you want a power of attorney, or authorization for a non parent, gives all the rights of a patent. And yes it can be withdrawn, but so can a guardianship.