Short summary for non-uruguayans: Uruguay started out as the Spanish piece of the land on the eastern side of the river Uruguay according to the treaty of Tordesillas, and became a disupted frontier between Spain and Portugal.
During the May 1810 revolution (Argentinean revolutionaries against Spain), while the capital city was a Spanish stronghold the local leader José Artigas sided with the Argentinean insurgents and founded the United Provinces.
Artigas wanted a federal system, but the Buenos Aires leaders wanted centralism. So Uruguay actually became a province of the Federal League.
http://en.wikipedia.org/wiki/Liga_Federal
When Uruguay announced its independence from Spain, it became annexed to Argentina.
Then Brasil invaded, and it became a Brazilian province for a short time, thus the parent comment.
How can we be sure? We know countries unify and we also know that countries split never to be unified again.