Step one: Set up a gmail account in your babysitter's name.
Step two: From that account, email her the following message:
You & I have a same first name, same middle name, and same last name. My life is same as yours. I babysit "J" [His name] like you. I look like you. I babysit different "J". I live in different universe which is quadrillion light years away from you. I have a special computer internet which radio ways are quadrillion light years per second.The least plausible claim in this email message is that there's anyone anywhere else in the universe like "J".