Hello, Jonas.
I think this is not a case related to dialect. In Brazil, we don't have dialects, but differences in pronunciation between regions and between generations. The "r" in brazilian portuguese can be pronounced like the "r" in italian or spanish (but in general not so stressed, it's a soft version) or the "r" in french and in general, it depends on the word: "carrinho" (cart) the "r" is like in french; "carinhoso" (affectionate) the "r" is like in italian; "rua" (street) the "r" is like in french and so on. But, like I said, we are a big country, so depending on the region or the age of the person saying the word, people can say "rua" (street) with the "r" like in italian. And, to make things more complicated, there are still other countries where portuguese is spoken, like Portugal, Angola, Cabo Verde, Moçambique, Macau, Timor Leste etc.