No, they shouldn't have, but that was kind of part of the "arc" for her character. When they arrived she was unfamiliar with them, their ages, interests, or anything. And the secretary/assistant or whatever she was being treated as this "servant" was also kind of a part of the "arc" for BDH's character. But that's one (of a handful) aspects the movie fumbled on, particularly when they apparently removed the scenes that were supposed to cause us to not like her in the first place.
I mean regardless if it was "right" for her to be left with the the kids or not, in the end, at that moment they were still her "responsibility" as just being the adult who was around them. And if she was being a horrible person towards them because the character was just supposed to be a mean bitch to everyone around her (kids, subordinates in the park) then the stuff with the kids is pointless. We don't know what was supposed to make us not like her. I mean, what if there was a scene with her going into the park Starbucks, making some bizarre off-the-wall order of specifics about the coffee she wanted, she gets it, takes one sip, slams it down, and then rants to the barista about all the ways she failed at her job and that's why she's some minimum-wage underling instead of something more meaningful?
Such an encounter has nothing to do with the kids but is part of the reasons why we're supposed to dislike her. She's on the same "arc" as BDH as being a high-powered, executive level person treating everyone subordinate to them as lesser people and being self-absorbed with their own executive goals and needs, and then having to find out that's not the right person to be. Only BDH rides her arc "up" as she comes out of it as a better person, learning the importance of stuff outside of her executive life and caring for the kids, and the secretary wasn't learning anything from the arc so she's riding it down and maybe even comes out of it a worse person so her punishment is getting picked up by the Pteranodon and then eaten by the Mosasaurs.