OK, there is a legendary King of the Britons that corresponds to our Cymbeline.
Kinda.
There was a ruler named Cunobelin. It’s said (because there’s not a really exact history here) that he ruled in the first few decades AD. Back to him in a moment.
A couple of plays back, we read Antony and Cleopatra, which kinda, in a weak way, was a sequel to Julius Caesar. Now, before Caesar suffered the Worst. March. Ever, he was one country-conquering machine. And while he was securing Gaul, he did make incursions into Britain. There wasn’t an occupation per se, but there was definitely an influence. Remember that ol’ Julius bought the farm in 44 BCE. He was succeeded by the Second Triumvirate of Antony, Lepidus, and Octavian. After the events of Antony and Cleopatra, Octavian proclaimed himself emperor and renamed himself Augustus. And Augustus–yep, the Augustus referenced in our paly here–continued to rule over the mainland during this time, leaving Britain militarily alone, and the emperor died in 14 AD.
Back to Cunobelin.
He wasn’t king of all Britain. Number one: there wasn’t a Britain (politically speaking) then. There were areas, each ruled by their own king. Cunobelin was successful in bringing together a couple of those states. Cunobelin also had brother, Epaticcus, who helped in the expansion and control over the tribes of Britain. The brother died around 35 AD.
By all accounts, Cunobelin’s relationship with Augustus was pretty good. There is no discussion of tribute paid to Rome. Augustus died in 14 AD.
Cunobelin had no daughter that we know of; he did, however, have three sons: Adminius, Togodumnus and Caratacus (the play’s sons Guiderius and Arviragus do not appear to be analogs for the historical sons). When Cunobelin died sometime before 43 AD, his son Caratacus continued his father’s expansionist policies. When he took over yet another of the states, however, the Roman emperor at the time, Claudius (the third emperor after Augustus, following Tiberius and Caligula) called for the invasion and conquest of Britain.
None of which is in the play.
When Geoffrey of Monmouth got around to writing his version of the history, Cunobelin’s name was transformed into Kymbelinus, and this version of the king did pay Rome tribute–but more out of love and loyalty (because Geoffrey has Kymbelinus being raised in Rome), than out of submission of the vanquished. Geoffrey also loses one of the sons, and renames them Guiderius and Arviragus, and these two head up the resistance to Claudius’ invasion.
Hollinshed changes the spelling to the “Shakespearean” Cymbeline.
So, history versus the play? Tribute paid to Rome since the time of Caesar? No. Daughter? No. Augustan invasion? No. Only two sons, and both of those kidnapped? No.
You cannot blame Shakespeare for faulty history-making when his sources did some history rewriting of their own…