I've seen a few "children can do xyz" mods so I figured it would be worth a shot checking if/where this mod could possibly exist somewhere. My sim kids are always holding tea parties with juice boxes and a teddy bear, but they can't be invited for actual tea parties at the actual tea set. Would there happen to be a mod like this, and where might I find it?

None that I know of, but just wanted to point out that it's not difficult through tuning or by using NRaas Retuner to unlock activities like this for children. The huge issue is that there are no animations present for them, so unless custom animations are also designed and provided, the kids would be horribly stretched out every time they interacted with the object. That's what is special about the "children can..." mods, as it is rare to find someone with both mod dev and animation design talent.