In hindsight, this wasn't too bad. We would get to spend an evening in one of our favorite cities, and we wouldn't have to attempt to sleep on a plane.
However, when we received the email, we were upset because we had tickets to a soccer (football) match, which we would miss if we accepted the flight change...and also because it happened less than 48 hours before we leave.
DH spent 2.5 hours on the phone with the travel company. They couldn't find one single option to get us to Brazil at the original time. He ended up paying an extra $1000 to get a flight to our second stop (where our flight to Brazil originates).
When he told me that, I figured that wasn't the best option (since we couldn't get any money back from the original flights). So, I spent 3 hours on the phone getting things changed back to the way they were.
So, now we're spending a night in big American city, getting to Brazil later than expected, and missing the soccer (football) match. However, the travel company was gracious enough to refund the charge for the extraneous flight that DH bought, and to get us tickets to another soccer (football) match later in the week.
All in all, 5.5 hours to get back to where we started was probably not the best use of our time! Hopefully there are no issues like this with our other flights during our travels!