I moved from VA to CA and the govt paid for milage, fuel, lodging, food, per diem, and to top it off they shipped my household E36 M3 which includes 3 transmissions and 2 engines (1uzfe and 4g54b). And minus the household goods shipment it probably cost them about $4,000. Lodging varies state by state, so does fuel and food. It helped the car we drove got about 500 miles to the tank and we took a slight detour to the grand canyon.
That's not all of it though.
Once we got here that's when the entitlements stopped. So, we had to find a house and live in lodging all while still needing food and fuel to look at places to live. Once we found a place we had to pay for first months rent, deposit (= rent), cut on all the utilities (expensive as E36 M3), buy groceries for the new house, (unexpected buys: California houses use gas dryers, ours was electric), car insurance on the west coast (including pnw) is way higher than the east coast (my insurance monthly premium tripled for southern California and was told if I had moved to Phoenix it would've quadrupled). Since you're not military you'll have to become a state resident of the state you moved to within a certain amount of time. Which means new license for all the drivers and reregistering your cars in that state (first time out of state registration is usually expensive).
Factor in the cost of living from where you're moving from vs your final destination. How easy is it to find a job, housing, become a resident, and lodging.
When it comes to us military moving across the country we can sometimes make money off of moves but moving to the west coast from the south east will almost always cause you to pay out of pocket because of cola and how many hoops those states require you to jump through. That's why we tell all the inbounds to factor in about $6,000 of initial moving cost for this location. Civilians who don't have such benefits I would tell them $15,000 or more. Especially more if they don't already have a job lined up as soon as they arrive.
Ideally you can budget move anywhere. But, it's much like an apparently affordable $3,000 LSX swap. Yeah you can buy the engine and trans for x amount. But, you'll be nickle and dimed beyond those initial buy in prices and how much of it is someone else doing for you?
Project the cost of this move for a worse case scenario the multiply it by 2.5 + a months living expense for every month you think you might not have a job.
Not saying you haven't thought of this. Just throwing it out there.
TLDR: You need monies to move a family and things across the country.