Interesting No full faith and credit clause constitutional issue as the state of residence does not explicitly recognize same-sex marriages, and even though Massachusetts does, and they were legally married there, they cannot use the residence state's courts to obtain a legal divorce.
What about changing the fact pattern just a tad? (lawyers love to do this) Some states do not allow 1st cousins to legally wed and others do, so what if they are legally wed in one state and then move and live in another, which does not allow 1st cousins to wed. Can that state then deny them the right to divorce if they decide to get a divorce in that state?
I predict this matter will go to the Federal courts.
Rhode Island high court rules against same-sex divorce
[JURIST] The Rhode Island Supreme Court [official website] Friday ruled [opinion, PDF] that a lesbian couple legally married in Massachusetts does not have the right to divorce in Rhode Island because Rhode Island does not explicitly recognize same-sex marriage.
In Chambers v. Ormiston [GLAD amicus brief, PDF; additional case materials], Rhode Island residents Cassandra Ormiston and Margaret Chambers sought to end their 2004 Massachusetts marriage. Lawyers for the couple had argued [JURIST report] that if the divorce was not permitted in Rhode Island, the couple's only recourse is to move to Massachusetts and establish residency for a divorce in that state, which lawyers said would be an unfair burden. AP has more.
In September 2006, a Massachusetts court ruled [JURIST report] that same-sex couples from Rhode Island must be allowed to wed in Massachusetts because Rhode Island does not expressly prohibit same-sex marriage through its state constitution, statutes or appellate court decisions. In February, Rhode Island Attorney General Patrick Lynch [official profile] issued a nonbinding advisory letter [PDF text; JURIST report] saying that Rhode Island will recognize same-sex marriages of state employees performed in Massachusetts. Lynch said that same-sex employee partners married in Massachusetts would be granted the same benefits as heterosexual married couples.
