The notification that babies are about to be taken away is a long-standing issue that predates Neighborhood Stories. There's a bug report marked "Needs Saves" here: https://answers.ea.com/t5/Bug-Reports/NEEDS-SAVES-Non-active-household-baby-taken-away-for-neglect/m-p/8813801/highlight/true#M125316
Basically, though, my experience is that if you're playing rotationally, or if you have adult children move out and have children, or if MCCC or Neighborhood Stories produces a baby, any time you're on the lot with the baby the parents (even if they're level 10 parenting) are playing video games, watching TV, and chatting with randos while their baby cries and cries and cries. The "taken away" popup sometimes hits you in the face the second you load the lot. If my Sims visit another Sim with a baby, they feed that baby no matter what other purpose they might be there for. ("Sorry, before we have our fistfight I apparently need to feed your baby. There. OKAY, LET'S BRAWL!")
