There's a mod that I use that's very close to what you're describing. It's called the
Babysitter mod. Basically, it turns your grown-up toddlers into an NPC for the game, which gives them their own likes in gifts and food, a couple of dialogues (you can talk to them now) and a lot of activities to do based on the schedule or babysitter you select. The activities include walking around town, learning and playing with Jas and Vincent as well as following their babysitter in his/her schedule if you choose to have one. The activities also vary a bit for every season.
Note that there's a couple of required mods you must install along the Babysitter mod for all of this to work. You can check the
Requirements drop-down on the Description page to see what mods are needed.
The only issue I have with the mod is that it's quite buggy, where sometimes the children will randomly not follow the schedule and even leave the house at night. If you can live with that issue, you'll probably appreciate this mod for giving your children a bit of life rather than just being running obstacles around your house all day long.