There is not much research on the Via Campesina yet. I just found this:
Martínez-Torres, María Elena/Rosset, Peter (2010): La Vía Campesina: the birth and evolution of a transnational social movement, in: Journal of Peasant Studies, 37 (1).
Nevertheless, a quick googling brought up this page: http://www.eurovia.org/
The Via Campesina-page will also have some infos...: http://viacampesina.org/en/
If you allow me this question: What studies on the Via Campesina did you find? I would like to do some more research on it, but -as I already wrote- it seems there is virtually nothing at all.