Can my daughter sign a notarized statement giving me temporary custody of my granddaughter without going to court?

In Arizona you can go either to the self service center at your local superior court, or you can go online (at least for the Maricopa County self service center) to this link: http://www.superiorcourt.maricopa.gov/superiorcourt/self-servicecenter/forms/powerofattorney/gn_ppoa1.asp Be sure your review the instructions and follow them closely. You may also choose to consult with an experienced family law attorney in your area to assist your daughter in preparing this power of attorney.

Yes, she can sign a notarized statement, but it will have little, if any, legally binding effect.

Yes, but she can withdraw it at any time and so can dad.