Does his company not have, resources per homes where you can live?
My friend has a Husband, who travels a ton, internationally. He is hardly home. Less than your Husband.
They move often.
He is in charge of international regions. Whenever they have had to move due to his job, both in the USA and in other countries, they always find a home & school first, then move. All of them. At the same time. And she has 3 school aged children. The Husband's corporation also, helps them.
Having kids in 1st grade and PreK, that is not an academic hardship. And socially, because they are younger, they can adapt and go to a new school, and adjust, easier. To me. Versus an older kid.
Then you have your elderly and frail Mom. Is she going to move with you all, too?
I would think so.
When exactly is your Husband expected to move?
Now?
Or can he also tell them, a time frame per when you all find a place to live? Or is the company going to put him up in a house or apartment, UNTIL you/his family, finds a place to live?
Then, once it is time to move... I hope it is not just you, who will be doing that and getting everything into place and the kids and your Mom and trekking to that other State? Husband also has to take time off to do that.
ETA:
Prolonging the move for you/your children will not eliminate stress of moving.
It just keeps it, prolonged.