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In a divorce both parties have rights to be protected and a legal representative to ensure that they are. Since you chose the analogy, why shouldn't secession be the same?
It would have to be fair in order to ensure a peaceful transition. You are correct in the fact that in this case, there would be no representation for the states or the federal government, so the Hague would likely be the only recourse for an independent party. We could also choose other states or countries as independent parties to ensure a peaceful transaction. The Hague just ruled on secession actually... they said that there is nothing that can prohibit it. Do you have a better solution? Under the current system, only the federal government decides for themselves(SCOTUS).

It would have to be fair in order to ensure a peaceful transition.

Something the Southern states were uninterested in back in 1860-61.

...so the Hague would likely be the only recourse for an independent party.

Or here's a crazy thought. Why not have both sides negotiate and agree upon a fair and equitable settlement of the issues of disagreement before separating? Again, something the Southern states were not interested in in 1860-61. They were bound and determined to separate in the most acrimonious manner possible.