The first issue is that you should be directing them to take care of the babies and to not just pick toddlers up and hold them.
The second issue can be caused by either a child from an inactive family being taken away by the social worker and causing rabbit holes to burp sims out like when I had that in older saves and those were ones that had become corrupted or it can be an overcrowded school if it's just happening at the school and that one would need awsomemod with the automated school assingment overide enabled in the config file if you want to actually stop issues from even happening to the schools as this solution is for preventing these issues.I use Mods to remove the NPC social workers and have story progression configured to run like the one in TS2 to control the population growth.There are other Mods that help if overcrowding does happen in schools if it's a minor case and awsome would prevent it from happening as you'd have to enroll all children and kids in school manually as they won't attend before being enrolled.