I don't do travelling light lol. It's harder now I don't have the pushchair and the kids are still just as accident prone. I am that Mum that has plasters in on of the pockets in her phone case, her purse and her handbag. I've never regretted carrying it, but it's bitten me in the ass a few times when I haven't had something.
I have a backpack so I have hands free for monsters, usually it always has a zipped sandwich bag with bubbles, a couple of colouring books or notepads, colouring pencils and stickers for when I need them to sit somewhere and be quiet, a pack of wipes, a pull up and some nappy bags in the bottom. A spare t-shirt of mine and a pair of leggings and a top for my daughter.
Then I add in my little zip bag which has essentials in it (sunglasses, lipbalm, mirror, suncream, glasses wipes, plasters, painkillers, allergy tablets, spare knickers for me and my daughter, spare underpants for my son, sanitary towel/inco towel, tampons, deodorant, tissues, hand warmer patch, hairband, hands free kit, charging cable and power pack for my phone, pens, a small roll of electrical tape and a small roll of medical tape, a couple of empty sandwich bags, a couple of folded carrier bags, scissors, usually some ribbon and the paddington tin which is filled with safety pins, velcro, hairbands and clips for my daughter, a trolley token and a strip of glow in the dark tape).
Then I add in her Minnie mouse bag I think it was intended as a wash bag but it works great to hold 2x spare pants (usually his because I can always put her in bigger pants but he can't be squeezed into hers), 2x spare socks, 2x pull ups, 1 pack of wipes, 1 pair of leggings, 1 top, 1 vest, 1 hairbrush and a couple of hairbands, suncream, a small tube of bite and sting cream, a small can of cooling spray, hand sanitizer, deodorant, glasses wipes, painkillers, allergy tablets and the radar key. This makes accidents and trips to the toilet especially on the trains easier.
I generally throw in one of those folded up waterproof mats, something like cereal bars, flapjacks or crisps and a couple of my fabric shopping bags and a couple of pairs of gloves in the other pocket and shove a bottle of water in the outside pocket.