Armenia and Turkey are two countries that have long had a fractious relationship, largely arising over the Armenian genocide of 1915, in which the Ottoman Empire massacred over a million ethnic Armenians. Recently, there have been moves towards some kind of rapprochement between the two countries. I do not know the details of the engagement between them, but it is interesting to note that the Armenian diaspora community (many of whom are descended from survivors of the genocide or of people who were expelled from Anatolia during it) seems to be very against the rapprochement.
Armenia's president, Serzh Sarkisian, has felt obliged to tour the Armenian diaspora, in an effort to head-off opposition to his Turkish policy. His success in this endeavour seems to be a bit mixed – earlier this week he had to be shielded by Lebanese cops from angry Lebanese-Armenian demonstrators. I do not know what exactly in the Armenia-Turkey engagement the diaspora are objecting to, but I find it interesting that the Armenian president finds it worth his while to try to secure the exile community's support for his policy. I am assuming that the Armenian diaspora does not get to vote in Armenian elections, but it still seems to be important for him to engage with them.
I am not sure if there has been any general research done on the role of diasporas in conflict situations. The other obvious one I can think of is the role of the exile Palestinian community in the Israel-Palestine conflict, but I understand that ethnic diasporas have been important factors in the Sri Lankan and Aceh conflicts. Working from first principles, I can imagine a strong diaspora to be a major complicating factor in the search for a settlement. On the one hand, they have relatively little to lose by the continuance of a conflict, while oftentimes they are not going to gain anything by its resolution. Diaspora interests will often diverge from those of the non-exile community, so a settlement that works for one community could not be acceptable to the other.
That is not to see diasporas as "bad", or as groups that have to be marginalised or blocked if a conflict is to be settled. If they are in a position to block settlements, then they should be engaged with as another actor in the conflict. Maybe it would be best to break the fiction of their sharing an identity of interests with the home community, and instead give them some kind of separate representation at negotiations. This might depend on the specifics of any conflict.
Stop press: Armenia and Turkey today signed an accord, though they were unable to agree a statement on it.
some random links:
ARMENIA: KARABAKH TALKS POSES BIG CHALLENGE FOR ARMENIAN-TURKISH RAPPROCHEMENT
Lebanon Armenians angry over planned Turkey deal
Armenians anxious over Turkish plan