Miss independent

My second daughter is super independent and extremely resourceful. But she is only 3. Sometimes her independence can wreak havoc. No matter what the situation is and what she might have done, she always has good intentions.
Example 1: one time when she was toilet training at age 2, we were eating lunch with friends on Shabbos/sabbath morning. All of a sudden she comes running over to me holding soaking wet undies. At first I assume she had an accident but the underwear was just too wet! I ran into the bathroom only to find she made and tried to flush it but dropped her underwear into the toilet instead! OY VEY.
Example 2: she always wants to help me with the baby to give him his sippy and help him in the morning. But she cant reach the crib so she usually just throws the cup at him, barely missing some body part or another.
Example 3: she wanted to serve the yogurt at breakfast so she went to the fridge to get the container and carry it to the table. Well the cover was slightly damaged (not her fault) but when she grabbed it by said cover, it spilled ALL OVER the kitchen!

I continue to let her "help" because I think it is a valuable lesson and I would never discourage helping. In the meantime I try to emphasize being CAREFUL since she could be a real help when she is. So i give her specific jobs i trust her with. For example, she's our official garbage bag replacement system. She has been going into the cabinet, opening the bag, and placing it in the bin since age 2. And she loves to wash veggies- something I don't think she can really mess up with.
So, I'll take the occasional mess for a helpful attentive child. Hopefully she'll learn to be a little more careful. For her sake. And mine.