Okay, let's just start with the definition of a diplomat: a person who can deal with others in a sensitive and tactful way.
Hmm, so then we have the main character - a woman who shouts right from the get go, and not in private, but in her office so half the building can hear her. Then, just as she is meeting with the US President, she has an altercation with her husband, and actually physically punches him in the face when he admits he doesn't want their marriage to end. So, all covered in twigs and dirt, having lost her temper violently over something relatively minor, does she sneak back into the mansion to tidy up a bit before talking to the US President? Nope, she just marches in, seemingly oblivious to the fact that she's just physically assaulted another human being, and looks like something the cat dragged in.
Add to this to the fact that she drops the 'f' word like a trucker; talks with her mouth full; refuses to wear anything except the world's most boring black trouser suits (you know the ones - they get worn by every woman in every FBI/CIA episode ever made); doesn't seem to care one iota about her appearance or anyone else's opinion, is often quite rude, and - unfortunately - you get a character who is about as far removed from a diplomat as you can get. I think a nail gun would have more tact and sensitivity.
Don't get me wrong, there is nothing wrong with the storyline, the acting or the production. The only problem I have is the main character and her credibility. it simply isn't believable that the US would make her an Ambassador to the UK, or that the UK would accept her... no matter her good intentions to make the world a better, safer place. She could have done that as someone behind the scenes such as advisor/analyst or something similar.
Incidentally, her on-screen husband, Rufus Sewell, is fabulous in the show. He is charming, sauve, polite and considerate: every inch,, in fact, the diplomat.