You may be right.
In addition to acting in an extreme and outrageous manner, the actor must act with intent or recklessness. In other words, the actor must intend to cause severe emotional distress or know that severe emotional distress is likely to occur. The actor can also become liable for intentional infliction if they behave with deliberate disregard to the high possibility that severe emotional distress will occur.
Sure sounds like intent to me, and there are at least two victims, the child and his mother.
The criteria you give for intentional infliction of emotional distress, added with her earlier statement about targeting Barron... sounds like grounds for a lawsuit.