Keep in mind if you get caught moving birds across state lines without the proper paperwork it can get you in trouble with agricultural authorities.
Repeating what Aart said, for emphasis. Saying it myself in BOLD
MOVING UNTESTED POULTRY ACROSS STATE LINES IS DANGEROUS AND IRRESPONSIBLE.
...and I say that as someone with strong libertarian (little "l", not the Party) leanings who is not generally inclined to look fondly upon Gov't regulations (though I've helped write them at times).
California recently had problems with vND (
virulent Newcastle Disease). It
required roughly two years to get it under control.
And the destruction of a lot of birds - more than one million. Efforts were hampered by irresponsible, ignorant, and/or uncaring individuals rehoming or otherwise
transporting birds across State lines for the bird's protection and/or as the beloved family pet - at risk to all the other birds then exposed.
No matter how well meaning, how loved your poultry may be to your family, transporting without testing is like pulling your grand parent from a diseased nursing home and placing them in another, with nary a word of warning to the new neighbors - only instead of risking a small number of human lives, you risk the well being of potentially millions of birds, the happiness of other owners in a broad geographic area, and the livelihoods of those who rely on commercial flocks.
Don't do this. Get tested.
(Separately, it sounds like you have little resources for transporting the birds in what will no doubt be a stressful move for the whole family, birds included. Recommend a few minutes with the family for a serious sit down with a goal of rehoming the entire flock, and replacing them when you've settled in at your new location. Have you even checked zoning there, to see if chicken keeping is allowed?)