Cross-jurisdictional judgments

A question I am pondering now as I work is that of cross-jurisdictional judgments. It is fairly common in a federal system (like the United States or Canada) for there to be some form of recognition by other territorial divisions of the legal judgments or determinations of other divisions.

For example, if you get married in Ontario, that marriage is recognized in Quebec, British Columbia, Alberta, and every other province, and depending on a variety of factors, by American states, such as New York and California.

This is not always true, of course. If you get married to someone of the same sex in Ontario, the chances of that marriage being recognized as valid in, say, Iran or perhaps Utah is likely to be negligible. And the opposite can also be true; if you get divorced in Ontario, that divorce will not be recognized in states that do not recognize divorce.

However, in any case, one can say in general that there is a reciprocal agreement between North American territorial divisions to generally accept marriage and divorce decrees, although not those between same-sex couples.

Where I am having trouble is with respect to the effect of those judgments. It's very easy to say that person X and person Y are married in Ontario, and therefore if they move to Hawaii, they'll still be married under the laws of Hawaii. It's also true to say that if they divorce in Hawaii, chances are, this divorce will be recognized when they get back to Ontario.

But what if, while in Hawaii, they created a divorce decree that stated that the issue of alimony would be decided by the court at a later date after both parties have filed information on their respective incomes, and then both parties went back to Ontario?

Would the Ontario Superior Court of Justice give full effect to this judgment, in effect treating it as a judgment of the Ontario Court, and proceed from there (i.e., requiring that the parties file information on their respective incomes and then make an alimony decision)? Would it set the issue aside entirely and conduct its own judgment? Or would it require that the parties go back to Hawaii and litigate the issue at question there?

If it chose the first option, on the basis of which law would it then proceed? Hawaii law, or Ontario law?

This is of course made all the more complicated by the fact that, even within Canada and the United States separately, not all judgments, records, or other determinations are carried over. If, for example, you receive a concealed carry permit for a firearm in Florida, it is not true that all other states would recognize that. They have a public policy concern in doing so, primarily which tends to override the full faith and credit.

The Defense of Marriage Act seeks to prevent same-sex marriages from carrying over from states where they are permitted to states where they are not permitted. Obviously, therefore, the issue is more complicated than it first appears.

The truth of it is, however, I'm not sure exactly what the answer is...