Just conjecture, but…I actually wonder if the image wasn’t ES’s way of “nudging” CS to stop and think about where his kids were.
CS clearly doesn’t respond well to direction, and ES knew he had all the kids with him at home while she was (I believe) at work, so she probably knew that asking him, “Hey, could you check to make sure you know where all our kids are?” could cause him to blow up (he seems like the type who’d likely perceive that as “nagging”). Since we know she had previously taken issue with his leaving the kids unattended in the car, I could see her sending the image of a child in a car seat to try to trigger something in his brain that might cause him to think, “oh, I’d better check to make sure all the kids are in the house.”
I mean, ES might not have really known CS’s plans for the day Parker died (and again, I wouldn’t be surprised if she felt like even asking him that simple question would trigger him to have a full-scale meltdown about feeling like she didn’t trust him) so perhaps she was sending the photo just in case he was out and about with the kids and might “accidentally” forget to bring them into a store with him.