I could definitely see the United States interfering more in Lusitanian affairs, but Britain? The United Kingdom benefits so much from having a strong ally in the south Atlantic, its pretty much the entire reason they can travel from their ports in the home islands to their important colonies in India, Indochina, and the Persian Gulf, especially since the Sinai canal was built so late in the Empire's history. Stopping at ports in Portugal and Brazil was the only real effective way to travel around the Cape of Good Hope, though I could definitely see American support for rebels in Portugal as a way for the upstart nation to block British travel. It's not like that would be the only time the Americans interfered and supported rebels in other countries.
Maybe not in the recent times, but in the past the british tried to stab the Lusitanic Empire in the back. During the XIX century, the British empire attacked many trade ships, pressing my country to abolish slave trade, and we did it - in 1870*, but in our own terms. Also, they tried to take the current central region of Isabelia during the Berlin Conference, wanting to fullfill the "Cape to Cairo" dream, but the fact that the empire had made a colonization policy in the region, inviting freed slaves and poor people from Brazil to settle in Africa made our claims stronger.
However, after WWII, the majority of the european powers began to lose control over their colonies, because ttheir european territories were devasted and they, different from Lusitania, failed to integrate their possessions with the homeland (the USA and USSR were helping the separatist groups, too). So now the Britsh Empire is dependent on us to keep the possessions they still have (their lost of all the almost all their territories in Africa shows this).
*OOC: in TTL, the abolition of slavery in the Lusitanic Empire was very similar to OTL abolition in Brazil (progressive laws that restricted slavery bit by bit), but began earlier, during the regency of Dom Miguel, and so ended earlier.
I doubt that Portugal alone will amount to much- iirc it was a net drain on Brazil's resources up until the turn of the century when the industrialization finally took off. That said...
This stinks of Lusitanian imperial propaganda. The Lisbonists* are idiots, that I'll grant you. But there's no indication that the Iberianist ideals would fail, and similar ideals have worked pretty damn well in Germany, Scandinavia, Peru-Bolivia, Italy and the even the USA- regional federation based nation's are just as stable if not more stable than colonialist empires tied together by a crown.
*Lisbonists are the movement for an independent Portugal, Iberianists support the unification of Portugal with Spain under the Spanish republic.
It's normal to foreigners not to know the real dynamic of the Lusitanic Empire. Our territories are not "colonies", but kingdons integrated to the union - as the official name "United Kingdom of Portugal, Brazil, Isabelia and Algarves" says. The only exception is Timor, which is a Princedom and don't appear in the name because of it.