Sorry, I don't think I can survive a disaster on $100 in food, water, supplies, and tools.
First, you need more than one light for a family. In a disaster, l.e.d. lights are the only way to go as it will be hard to get more batteries when stores are closed or cleaned out. I would recommend a Fenix EO1 for every household member, a 4D 145 lumen Coleman Cree packaway lantern to use in a common room where everyone can talk, hang out, or play games, and a Fenix L2D CE for a bright light to check for damage, looters, or missing people or pets. You'll need a good stockpile of AAs, AAAs, and Ds for this setup. Then you need emergency equipment besides lights. A good first aid kit is a must. Costco sells a good American Red Cross first aid kit for about $25. It includes survival supplies including a whistle, emergency blanket, light stick, disposable handwarmers, water pouch, emergency poncho, and face masks, as well as well thought out first aid supplies. Then you need a supply of water big enough for the family to last through the disaster. The rule is that you need at least a gallon per person per day. An emergency will usually affect you from 72 hours to two weeks. It's best to be prepared for a week or two. Two weeks of water for a family of four is 56 gallons minimum. You need more water if you have to rehydrate food, clean, or bathe. All food should be canned as it stores well long term, doesn't require refrigeration, and doesn't use more water to cook it. Don't assume all disasters will let you stay in your home or that shelter will be available elsewhere. A good family tent and sleeping bags should be part of your disaster kit. Don't forget that you may not have a way to cook your food. Have a stove that takes multiple types of fuel or a wood burning stove such as a Sierra Zip Stove. Bring plenty of spare fuel. Some backpacking stoves will run on white gas, kerosene, gasoline, diesel, and also pressurized butane canisters. You'll also need a good supply of matches, a lighter, and a multitool with a good can opener. Water may not be safe to drink. Get a good handheld filter or purifier. I'd suggest a First Need water purifier as it's the only one that doesn't use iodine. Prolonged use of iodine for over 2 weeks isn't safe for you. Don't buy into "purifiers" that don't filter the water first. They won't remove chemicals that are unsafe. If you get all of these things, it will probably cost closer to $500, but it will be worth it for long term survival. Dont forget to have a full tank of gas in your car. That alone may cost $100. I think you'll only be prepared for maybe 72 hours or less realistically if you only spend $100 and that's only if you stay in your home.