They may affect practical timing and require reassessment of the principal’s proposal. Family permissions still depend on each person’s individual status and circumstances.
Keep individual permissions explicit
Qualifying L spouses are employment authorized incident to status with appropriate documentation. L dependent children are not work authorized solely through that status. Review school, remote-work and travel plans rather than assuming the company’s revised schedule resolves them.
The disruption households actually experience is not the assignment changing; it is finding out late. A start date slips by three months, and the family has already given notice on a lease, enrolled a child for a September start, and accepted a job offer that begins in August. None of those decisions was unreasonable, and all of them were made against a date that was always provisional.
Ask the employer which parts of the schedule are fixed, which depend on a step nobody controls, and who will tell you when either moves. Then make the commitments that can be unwound, and hold the ones that cannot. On permissions, the position does not change with the schedule: a qualifying L spouse's employment authorization runs from that person's own status and documentation, dependent children are not work authorized on that basis, and school enrolment questions are answered by the school district rather than by the assignment letter.