Three people move through one initial application, so the family's readiness sets the pace: a missing document for the child holds the household. The company should sequence internal approval, the online application and US$45,000 in fees, and document submission, then wait. Vetting, visa availability, and any interview are outside anyone's control, and published week counts are not commitments.
Separate the work date from the school date
The employee's start and the child's school enrolment are different problems with different deadlines, and treating them as one produces a plan that fails twice. Ask the family which date is genuinely fixed, then decide whether anyone travels ahead or the household moves together. Avoid non-refundable deposits and lease commitments until the status permitting the move exists, and review the plan again after vetting concludes.
Add one further rule about how a date is communicated once anybody outside the household hears it. A school registrar, a current employer and a landlord all act on a date the moment it is given, and a date offered as a plan is remembered as a commitment, so nominate one person to state dates externally and one form of words that separates what is fixed from what is merely expected. Then hang the notice period on the current job, the school registration and any tenancy notice on a single stated milestone rather than on three different ones, so that a slip moves one set of consequences instead of three.
Hypothetical example: a household agrees that only the employee gives dates to the current employer and the school, always as a stage rather than a month, and a six-week slip costs one conversation rather than three sets of arrangements that have to be unwound.