I would not drive 4 hours to take a child for whom I’d been told needs to go to the emergency room. Regardless of the quality, at that point stabilization, etc. would be on my mind - not the best in the world and 4 hours away. That stuff comes later.
The article you linked tells a totally different story. From that perspective, she didn’t take her child to the emergency room because she was afraid she’d be arrested on a variety of pending charges. Instead, she just took off, but because of the multi-state search for her, she eventually got him to a hospital.
The original article also doesn’t refute the information that the infant was dehydrated. It provides a reason (dysfunction of the esophagus) and another symptom (elevated white blood count).