I've posted on the sinner's prayer before and this phraseology of asking Jesus into your heart has been something i've avoided in my home. Probably why this post caught my eye . . . after all we want our kids to have an accurate grasp of salvation.
"My concern in this book is not on what words we might use to express our faith, but that we understand saving faith and how we can gain assurance that we have it. Many Christians see salvation as a transaction one conducts with Jesus (signified by “inviting Jesus into your heart” or some equivalent) rather than the beginning of a posture they take toward the finished work of Christ."I'd encourage you to read the whole post