Hey, it's a great start. You will continuously add (and remove!) things over time, and at the end of the day only you can decide what to include.

Since you're oriented towards being on the move, don't worry so much about the pack until you get the footwear and clothing sorted. In your car along with your pack, you can include a good pair of broken in hiking boots, underarmor type moisture wicking underwear, and other proper clothing that you can change into from whatever you happen to be wearing.

Second, while people tend to like self sufficiency, odds are you won't have to make the 400 miles on foot even without a vehicle. Other than hitching a ride (with associated risks), sometimes a couple hundred dollars in cash will do what a whole bag of goodies won't when it comes to being able to keep you and yours safe. It means a hotel room, or a bus, and food.

Whenever you get the gear the way you like it, take a couple days and hike some legs of the Appalachian trail. It will give you real experience lugging the pack around, and the experience will help volumes.

Here's my recommendations, for what it's worth
-Proper hygiene kit oriented towards you being on the move, including but not limited to (you already have some of this) Gold Bond powder, Bordeaux Butt Paste, Bodyglide, Moleskin, Sunscreen, Bug Repellant, Feminine Hygene stuff, wet wipes and TP. Spare socks.

-For shelter, bugs are your primary concern much of the year. Because you're with company, you'll probably want a multi-person shelter like a small trail tent with mosquito netting. Keep in mind inexpensive tents tend to leak, you might want to treat it with waterproofing spray. It can get cold enough in the winter that hypothermia is a concern so you'll have to decide how you want to handle that as well.

-For water, you already mentioned fixing your situation there. I prefer a large source (2 liter canteen or 3 liter bladder) and one or two smaller sources (canteens or nalgene bottles with cups) for flexibility in cooking and purifying. Purification tablets will work for the majority of water you might find. Filters are nice but can get very expensive, for a kit you'll only be using in an emergency you might add just a couple of water filter straws (like lifestraw or the ones by frontier). These should be used in conjunction with chemical treatment or boiling and only by themselves directly from a source if all else fails.

-A good knife doesn't have to be expensive. A more robust (~$15) combined with a proper hand saw will be able to do almost everything you'll need when it comes to processing wood. Maybe throw in a multi-tool (good for disassembling your car if you need to, grabbing hot or sharp items, cutting wire, etc)

Other practical items include a spare phone battery (or external battery pack with sufficient capacity to last 2-3 days), a pay as you go phone for your daughter, a couple of FRS/GRMS radios maybe.

Everyone needs to start somewhere, I've been tweaking mine for years, I still change and improve things here and there (and I went WAY too heavy at ~65 pounds, I need to cut mine down lol)