Nanny here.

I don't do diaper bags. There is no need for them and there is just too much fuss factor involved.

I concur with those who say to simply get a diaper wallet. I am happy to use one if the family uses one of those. If not, I put two spare disposable diapers and a little travel package of wipes into a gallon ziploc bag, with another gallon ziploc inside.

I am now prepared for two diaper changes!

Puke? Blow outs? Either diaper wipes or water from the sink if there is a sink. Kiddo can wear damp clothes dry. Won't hurt 'em. Everything else is simply to protect the ego of the parents from judgy other parents. Let judgy other parents judge; they are only hurting themselves.

Toys? That is what the world is for! Let them pick up a pinecone, play with house keys, explore the texture of upholstery. There is no need for dedicated toys.

If leaving for a significant enough period that kiddo will become hungry, I might also bring along a soft-sided lunchbag filled with whatever food is applicable to the age of the child (pumped breastmilk in bottles, formula + water + bottles, stage 1 or 2 baby food, toddler snacks). But I don't consider that to be "diaper bag" fodder, anyway.

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TL;DR -- Use a bag that you already have and simply load modules as necessary.