I love this pose as it aligns the entire spine.  Sam Dworkis expounds on the healing value of this pose in his book, Restorative Yoga.  We often find children slowly spinning with arms swinging about their body and it reminds me of when I would rock a baby on my hip to calm myself as well as the baby.
What I discovered after many years of using this pose is that it is an excellent precursor to tree pose.  As you slowly spin side to side you are shifting your weight from one foot to the other.  This allows each foot and leg to take on the majority of your weight while continuing to have the other foot planted for stability.  As you practice this pose notice how it requires both sides of the body to be responsible for stability and allows a child with hemiparesis, one sided weakness, to strengthen the weaker side of the body.  Soon the child will be able to stand on one leg for tree pose with just the toe tip of the other foot for varied amounts of stability.

While in puppy pose, ask the child to pant like a puppy.  This will look and sound like short quick breaths, much like fire breath.  This helps them to refocus on their breath.

Because I have been a pediatric Speech Pathologist for 37 years I meld language and yoga with every class I teach.  Yesterday while teaching a group of four children I teased them by asking them to sit "criss-cross cranberry sauce."  Thinking this was funny, we launched into a laughter filled activity of fill in the sauce.  To enhance the activity we chanted and created a complimentary mudra.  We slapped our hands to our knees while chanting "criss", crossed our arms and slapped the knees to "cross" and repeated this with "cranberry" and "sauce".  This is what we created;
                                           

Spaghetti Sauce
Chocolate Sauce
Raspberry Sauce
Alfredo Sauce
Marinara Sauce
Pesto Sauce
Blueberry Sauce
Mango Sauce
Caramel Sauce
Peanut Sauce
Pineapple Sauce
Pie Sauce ????
Cheese Sauce
Zucchini Sauce