If I understand correctly:
* Mom doesn't plan to move for more than a year.
* Your DH wants primary custody of the kids for a full year before she moves...
* And 50/50 custody permanently, after she returns?
How will he visit the kids when they're overseas and who will pay for travel?
Is the country a signatory on the Hague Convention re International Kidnapping? Even if it is, I'd petition the court for her to post a bond, that will be returned to her when she returns the children at the end of the year, as promised.
What would stop Mom from applying for citizenship for herself and the children? A year is clearly a relocation, not a vacation. For example, if I move to another state with my kids for a year, the new state can assume jurisdiction over their custody. What assurances does your DH have, that this can't happen in his case?
I would never consider letting her do this without a court order. Even if your DH and his ex agree to terms and file it with the court, instead of fighting over details at a hearing, there must be some avenue for enforcement of terms, which a simple agreement - even in writing - between the parties will not provide.
Personally, I wouldn't agree to that on any terms:
* If Mom lives close enough now, to offer her EOW visitation if your DH had custody for a year, then presumably the kids see your DH pretty regularly now, right? It's not good for them to spend a year seeing him very infrequently, or not at all, if that can possibly be avoided. If a soldier father is separated from his kids because he's sent to Afghanistan, there's an understanding that he didn't want to be away from them and a certain bond, in the mutual yearning to be reunited. But in these circumstances, the kids would be aware their Mom felt like whatever's drawing her overseas was more important than their contact with their Dad...and they'll know your DH could stand to see them go. Yuck!
* If Mom changes her mind and wants to stay, your DH might have little recourse to prevent it! He could argue that she's breaking her commitment to him, but the court will still be more concerned with the best interests of the kids, which might not be served by uprooting them from the life and school they will have spent a year getting accustomed to; nor by taking them away from their mother, if the only thing she's done wrong is wanting to prolong an arrangement your DH agreed to.
* If it is acceptable for the kids to be away from a parent for a year, why can't it be her? Why can't the kids spend that year with your DH, until she comes back? That would provide a lot more stability for them, if you guys live near Mom. And asking for them to stay here and maintain their lives and friendships, while she goes, will be A LOT easier to get a judge to agree to, than asking to bring them back from overseas after a year, if Mom decides to stay.