"Emotion Coaching" is a form of coaching that primarily aims at increasing emotional maturity in the coachee.
Emotional Maturity
Growth
How to define "Emotion Coaching" and why the term is problematic in the context of parenting
Youtube
Soundcloud
Soundcast
Other Definitions
"Helping children and young people to understand the different emotions they experience, why they occur and how to handle them." (Gottman 1996)
Examples
Gottmann Institute: "The Heart of Parenting"
Emotion Coaching UK
"Emotion Coaching" should not be used in this context.
"Coaching" is not an adequate term to use with children while referring to parenting.
Using a general term and automatically applying it to a narrow use case / scenario, i.e. children, is not good practice in terminology.