Not everyone ran to #vanlife as happy as a hippie – sometimes economic or other pressures force one into living in their vehicle. In this situation we are focused on functional, not fancy. You are doing what is best for you and your family right now; you are not in competition with the Instagram “influencer” crowd.
First things first, let's reframe the situation a little bit. These perspectives may help you cope with the new stresses:
You will need a place to sleep. Your first few nights in the vehicle will likely be rough as you get used to the idea. Many people recommend earplugs and eye mask to block out light from streetlights, headlights, etc.
You will need a place to pee. A gatorade bottle or similar is common. Women may want to use wider-mouth jars. You will also need a place to poop. With any luck you will have access to a public restroom. If not, a couple grocery bags (doubled up) will do; tie off and dispose of in the trash. You might also dig a cat hole if you are in a place with grass or soil. If you have room, a bucket makes the process more comfortable.
You will need water to drink, to clean the vehicle and yourself up. Empty soda bottles are tough and hold water well. Rinse them out and fill in water fountains, spigots, sinks, whatever. If you have space to store gallon or larger jugs, water refill kiosks are relatively inexpensive. Heads up: “milk jug” style jugs are brittle and degrade quickly. You can buy water in them but don't use them for long-term storage.
You will need food to eat. Fast food is extremely expensive. Sandwiches made from deli supplies will be inexpensive. Since you probably won't be able to cook yet, focus on foods that can be eaten cold. You'll need a good manual can opener in any case. Peanut butter is a great bang-for-buck. Since you likely will not have a fridge, leftovers should be kept to a minimum. Buy only what you can eat.
You will need to wash yourself. You might bring a rag into a public restroom (bring a baggie so you can put the wet rag in it on the way out), pour some water into a bowl, use wipes. etc.
You will need a way to dispose of trash. Stuff trash inside other pieces of trash; loose bits inside jars and cans, for example. Toss trash into receptacles whenever possible.
You will need a place to park for the night. If you are in a city this typically means stealth camping. If you are on the highway you can usually sleep in a rest area then move on. In rural areas (particularly out west) you may be able to boondock.
You will need a place to do laundry, usually a laundromat. Leverage the free wifi if available. Carry your own detergent as it is obscenely expensive by the packet. Save your quarters for doing laundry.
A smartphone is extremely useful, even a cheap one or one that is not activated or on a plan. Cheap new smartphones can be found in prepaid sections in stores, and used ones can be found in thrift stores, pawn shops, etc. Verify it is not password locked and that it boots up before purchase.
Once you have your smartphone you can use public wifi for internet. Even though libraries, cafes, etc, are closed they likely still have wifi in the parking lot.
Once you are online with wifi you can get a webmail address like gmail or yahoo. Google offers free phone numbers through Google Voice, and those numbers can be used for text, voicemail, and sometimes phone calls depending on the setup. You would only be able to access the text/voicemail when on wifi, but it's a good way to stay in touch and the phone number looks like any other phone number. You can also do chat and video calling over your google mail account.
Tablets are functionally like large smartphones, and may make web browsing and forum participation easier. If there is no built-in microphone you may be able to use a bluetooth headset or corded headphones with mic to make phone calls.
Note: with some open wifi systems you have to connect to an unsecure website like http://m.cnn.com (not https) in order to get the connection agreement to show up so you can click on it.
For privacy, you can use a sunscreen in your front windshield and cut-to-shape cardboard (preferably dark or painted) on side windows. Hanging clothes up in the window is a sure giveaway.
For power, most charging for small devices like phones and tablets will be by USB. Some newer vehicles have USB jacks built in. If not, you can find ones that fit into the cigarette lighter in dollar stores and similar. Charge as often as you can, preferably while driving. See this discussion of power options. If you will be going to work or public indoor space regularly a small battery pack and extension cord may serve you well.
A gym membership will get you a place to shower, use the restroom, use wifi, etc. And exercise if you are into that.
If you don't have a license or photo ID get that immediately, as a lot of other things depend on it.
If you have a car note, pay that first and insurance first. You don't want your home to get repoed!
Register for social services in your area as quickly as possible, as there can be some lag. Food banks, unemployment, food stamps, etc, they exist for precisely this reason. They were funded by you and by people like you for situations just like this. Don't be a hero or a proud idiot.
If you still are going to work, do as much of your device updating, bathroom-using, washing-up, trash disposal, ice-making, and water filling there as is appropriate. Example: rotate in freezer packs when you get to work and put them back in your cooler at the end of the workday. Take a full container of water with you every day when you leave.