I don't think there was much of a Portuguese republican movement at this point; they hadn't suffered as terribly as the Spanish had during the Napoleonic Wars, so their liberal movement was still very much enlightenment oriented at curbing the powers of the king and introducing constitutional rule. Even in Spain, I think the Republicans remained a fringe movement and it was mostly those who wanted to do away with absolutism and restore the Constitution of 1812.
At this point, the Portuguese want the restoration of pre-Napoleonic rule, with Brazil effectively demoted to a colony. But It's a little late to turn back the clock and will definitely promote issues... they want their king and Cortes back, essentially. Even just the king is fine, many might even tolerate pre-war absolutism if he'd just come home, so to speak. The English military governor is awful and they want the British out, nice allies as they've made over the years. Brazil can go back to as it was.
You'd think the liberal movements would work together, but they are rather splintered. 1815 is the time of reaction, and the Congress System has firmly restablished crown and altar absolutism on the continent, or at least tried. France's constitution is a laughing stock and England has always been an aberration to the rule. One also can't forget that countries that quickly stray from this norm typically find themselves under the foreign bayonet and the true system restored. It hasn't been tested yet, but the Great Powers (minus Britain) had no qualms invading sovereign nations to squash rebellious movements (see: Naples in 1820; Spain in 1823; even as late as 1830, Austria had intervened with Italy, and in 1848 Russia in Hungary, although by 1830 the Congress system was dead).