I wouldn't credit either of them (Rachel or Ellie) with having "the Shine" for sensing that things were awry with Louis and the cat. No more so than I would credit you for having the Shine when you know that someone in your family has had a bad day, or know that your pet's just not feeling well today.
Living with someone, or a pet, for a long time usually includes developing a sense about them. When their behaviors change you just know something's not right. It may not be well defined and you may not have a clue what's wrong, or even how you know. Still, you know.
Children sense it more than adults because they're wired that way - noticing tiny clues from close people is part of how they learn acceptable behavior. The "home-maker" is often sensitive to the "bread-winner" as well, since they are dependent on them to keep the finances for the household's well being. (Note that "home-maker" and "bread-winner" are functional terms, not gender-related terms.)
This is one of the times when Mr. King didn't need to create, ascribe, powers, or "the Shine," to someone for his story to work. All he needed to do, for that aspect, was make obvious to the readers what they have probably experienced many times before. And then promptly forgotten as well.