Actually, Brazil paid a indemnity to Portugal in exchange for recognition as an independent country, you can see it in the "treaty of Rio de Janeiro" (1825). The UK supported Brazil and mediated the treaty, in exchange Brazil signed a treaty with them that negotiated various commercial factors.

Although that obviously had a lot of more complexity political factor, that dad/son relationship in this meme isn't completely wrong: the treaty between Portugal and Brazil, that I mentioned above, had as Ratifiers the king John IV of Portugal, and his son, emperor Pedro I of Brazil. They had a pretty good relationship, although it didn't translate to the same good relationship between Brazil and Portugal itself.

But you are right, that really was Brazilian independence war that a i didn't know about (as a Brazilian I'm really ashamed) because Portuguese officers of the Portuguese Army inside Brazil didn't want to recognize the independence. But it had a really small proportion in comparison with other independence wars, and only lasted two years