Those are triggers for most people, honestly, and I've found they happen with children no matter what you do. There WILL be waste, noise, and mess.
You can try to limit it by child-proofing and being playful. You can take regular breaks from it and teach them to help clean up. But it will happen, so learning how to cope with it without screaming is a better place to start than trying to keep it from happening at all.
It's all about managing your expectations and own big feelings.