Hello Lisa. There is no set "law" regarding which parent must pay for the travel expenses of the children in this type of situation and the issue is usually worked out between the parents or the court will make a decision based upon all of the facts and circumstances surrounding the case.
I would argue that she should have to pay for the travel expenses because she made the decision to relocate with the kids, and if she was the one who caused the marriage to break down, I would throw that argument in there as well, and he should have a good chance of having the court decide that she should pay a majority of the travel expenses -- but do not be surprised if the court splits it down the middle and rules that the expenses should be split 50/50, particularly with dad in the military and step-dad in the military (judge will know that their salaries are probably not that high and not that far apart).
Practically speaking, though, the main consideration is that whatever agreement he enters into now will follow him wherever the ex is relocated to and wherever he might be relocated to (assuming all parties remain in the military) -- and an order issued in Washington state is good in every state -- so if either party moves again (or several times), the other party simply takes the Washington court order into the nearest court in whatever state the other party is located in and "domesticates" the order -- and then it can be enforced wherever either party is located. And, no matter who agrees to pay for what travel expenses, such an agreement is not like child support where the child support enforcement authorities will hunt down the parent who refuses to pay the travel expenses and make them pay through wage garnishments, incarceration, etc. -- this agreement will be enforceable only with contempt orders in the civil court - and if either parent refuses to pay the travel expenses (or reimburse for same), the matter will end up going back into a court room with a judge telling the non-compliant party "please pay this" the first few times the judge sees the case -- and then eventually a contempt order and a wage garnishment may be issued -- but the payments under agreements like this are more like civil judgments that the party who owes the money gets chased and chased and can dodge for a long time (much like a credit card debt).
My point in telling you all of this is that no matter WHAT agreement he enters into or the judge orders for payment of travel expenses, if his ex does not have the money, she will simply refuse to send the kids and it will take him several years to chase her through the courts to get reimbursement (if he makes the payment) or, if he cannot make the payment for the kids to travel, then he will simply be denied the visitation with them until he can chase her through the court system of wherever she happens to be located to force her to step up to the plate and send the kids to him (unless he pays for it himself).
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