Hello Peewee B,
No, it doesn't contradict what you've read, you just misunderstood what you've read.
While here in Brazil you clearly are subject to all of the Brazilian criminal and civil laws, just as you would be wherever you go.
You are subject to a foreign Court Order, that is legally binding in UK, and if registered with the courts here in Brazil under a process called "Homologação da Sentença Estrageira de Divorcio" can even be enforced here in Brazil.
If the Order is not registered here in Brazil, you aren't going to be subjected to any penalties here in Brazil even if you are in violation of the Order. If your child's father is in violation of the Order by virtue of non-payment of Court Ordered child support it is highly unlikely that he's going to go to all the trouble of registering the Order here just to force you to return to the UK twice a year. At any rate even if he did, you would have the right to representation in Brazil and his claims would probably be laughed out of Court since he is also in violation.
That said, if you want to vary the existing UK Order, the only place that you can do that is in the UK. Brazilian Courts have no means of making Extraterritorial Orders, just as the UK has no such authority. It is all a matter of international reciprocity, and applying for enforcement of a foreign Order.
Exactly how long have you resided in Brazil? If you've had your permanency for more than one year, you can apply for Ordinary Naturalization with a reduced waiting period of 1 year residency, as opposed to 4 years others who are not married to a Brazilian citizen or don't have a Brazilian child. If you've lived here for more than 4 years you can also apply for naturalization for you child. If you are both citizens then the child's father could huff and puff until he's blue in the face, but there is virtually nothing he could do here in Brazil.
If you don't plan on returning to the UK, where you would be subject to the Order, I'd really suggest applying for citizenship for yourself and your child, then tell the father to take a hike. Since he's stopped paying child support, it's highly unlikely he'll be conscience stricken and miraculously start paying again, so you won't be losing anything to tell him to take a long walk off a short pier. Why should you worry about catering to somebody who is already a "deadbeat dad?"
Cheers,
James  Expat-blog Experts Team