For those who are searching for more opinions on the Catholic social teaching in regards to unions and the current events in Wisconsin, the Social Agenda, put together by the Acton Institute, is a great resource. The Social Agenda covers a wide range of topics, including unions, and, is a collection of central statements of the Roman Pontiffs from papal encyclicals, apostolic letters, and Conciliar documents.
Within the Social Agenda the right to unionize is recognized:
281. All these rights, together with the need for the workers themselves to secure them, give rise to yet another right: the right of association, that is, to form associations for the purpose of defending the vital interests of those employed in the various professions. These associations are called labor or trade unions. The vital interests of the workers are to a certain extent common for all of them; at the same time, however, each type of work, each profession, has its own specific character which should find a particular reflection in these organizations. (Laborem Exercens , n. 20)
The Social Agenda further explains Catholic social teaching on unionization and certain limits unions have:
283. The civil authority itself constitutes the syndicate as a juridical personality in such a manner as to confer on it simultaneously a certain monopoly privilege, since only such a syndicate, when thus approved, can maintain the rights (according to the type of syndicate) of workers or employers, and since it alone can arrange for the placement of labor and conclude so termed labor agreements. Any one is free to join a syndicate or not, and only within these limits can this kind of syndicate be called free; for syndical dues and special assessments are exacted of absolutely all members of every specified calling or profession, whether they are workers or employers; likewise, all are bound by the labor agreements made by the legally recognized syndicate. Nevertheless, it has been officially stated that this legally recognized syndicate does not prevent the existence, with out legal status, however, of other associations made up of persons following the same calling. (Quadragesimo Anno, n. 92)
The Social Agenda is a great resource for not just the current state of affairs with unions but also to explain Catholic social teaching on topics such as the environment, the economy, the role of the state, poverty and charity, and many other critical issues.