What if queen Victoria had married with Pedro II of Brazil? We would have a United Kingdom of Great Britain, Ireland and Brazil?
(Sorry, I please move the thread to Alternate History Discussion: Before 1900)
It's simply impossible and never considered by both parties. Also, this is what the Brazilian Constitution said:
Art. 1. The Empire of Brazil is the political association of all Brazilian citizens. They form a free and independent Nation, that does not allow any kind of union or federation that opposes its independence.
And:
Art. 5. The Apostolic Catholic religion shall remain the religion of the Empire [...].
Marriage with non-catholic royals in Brazil was impossible, so was marriage with anyone who had real chances of becoming the monarch of a foreign country.
Lastly, Victoria was quite older than Pedro II: she was born in 1819 and he in 1825. By the time the Brazilian government started looking for possible brides for him Victoria was already married.
HOWEVER, it's worth noticing that Victoria considered Pedro II a handsome man when both met for the first time in 1871 and she took the trouble of visiting him (not the contrary) in the hotel he was staying only to give him the medal of the Order of Garter and kissed him in his cheek when she did that. People around were quite amazed because she was already famous for her seclusion since the death of her husband.
Thus, there was no lack of interest from her part, at least...