Well, Trollope is no fan of America, it's safe to say. At the end of the report, she admits that when she travelled to America, she was fighting with her husband, and they were struggling for money, so she wasn't really able to feel happy in America, but she feels that her opinion would not really have changed even if her personal life were better; she genuinely detests American fashions.
The book is even titled in a way that draws attention to Trollope's main critique of America—they have abandoned European manners. In America, the notion of having to be formal seems stuffy, pretentious, and silly, but in Europe, it's still the way life is. What's interesting to consider is that the year was 1830—almost 200 years ago, but even back then, Trollope's opinions about America are still represented around the world. Many people have historically regarded America as a licentious, indulgent place where people do whatever they want all the time.
Whether an American should be offended by this opinion is really up to the person, because what some people call indulgence, other people just call freedom. In other words, any criticism against America could actually be a compliment in disguise. By saying that America is non-traditional, Trollope hopes to insult America, but if America is cutting-edge and revolutionary, that also has its merits. These are strictly matters of opinion, but in any case, Domestic Manners is a fascinating, very fun book to read now, almost 200 years later.