(((hugs))) I wish I knew the magic words to get easy child to listen to you. I am having the same difficulty with my sister. My niece shows major signs of Autism Spectrum Disorders (ASD), my sister is a nurse, yet she won't have her evaluated.
Our school district pushes pre-school evaluations very hard so that almost everyone takes their 3 year old to the screening. It is seen as a very social event. While they spend most of their time screening perfectly healthy kids, it does allow them to catch some of the ones that would have slipped through until kindergarten or 1st grade. Do your schools do something similar?