Not at all. It sounds different from European Portuguese, similarly to how American English sounds different from British English, but they are the same language, and mutually intelligible.

There are local dialects influenced by the languages you mention and others, but Portuguese is Portuguese, like English is English, with the normal variations you would expect from a language widely spoken around the world. European and Brazilian Portuguese native speakers can communicate with each other easily, share TV shows, etc.

Of course this is anecdotal, but my wife is Brazilian (from Minas Gerais) and struggles to talk with European Portuguese people (sorry!), and needs subtitles to understand it in a film.

Even in my Portuguese textbook it says that there is significantly more difference between European and Brazilian Portuguese than between UK and US English.

No need for apologies :)

I think the main issue you are alluding to is phonetic. European Portuguese speakers tend to really close their vowels, while Brazilian speakers open them. The end result is that it is easy for Europeans to understand Brazilians, but not necessarily the other way around.

I have seen this happen with English speakers, by the way. I remember a friend from the US needing subtitles to follow a British comedy show.

Would your wife have any trouble reading this, for example: http://publico.pt ?