Is The Isle Of Man A Country In Its Own Right, Or Is It Part Of The UK. Also, Why Does The Flag Have 3 Arms?

Yes the Isle of man is a completely independant territory with its own laws, judicial system and taxation system and is not park of the UK, but is a commonwealth country.
The Isle of Mann has long been one of the best regulated offshore centres in the world. Financial services and family and company trusts occupy the majority of the isles business focus.
The IOM located in the Irish sea, equidistant from Scotland, England, and Ireland, is 30 miles long and 9 miles wide and is famous too for the many films shot there, and motor racing .
The separate taxtaion system has allowed it to flourish and the Manx pound is a proud reminder of this.
The three armed man originates from the early coat of arms. is is displayed everywhere on the Isle and in advertising.

The Isle of Man (or Mann) is not a part of the United Kingdom, it is a dependency of the British crown. The citizens of the Isle of Mann are covered by law as British citizens, its citizens are known as Manx. Through an agreement between Britain and the European Union, those islanders who declare their British citizenship may enjoy free trade, living rights and travel into the European Union. Those who wish to be classified as Manx, have a special notice in their passport which prevents them from this right.

The three legs of the Trinacria are the three legs of man. Having been invaded and originally it was a Norwegian island of the Hebrides, Mann has a sense of humour about its flag. The three legs relate to its position between three nations. The following saying is supposedly why:

With one leg I spurn Ireland,
With the second I kick Scotland,
And with the third I kneel to England

The Isle of Man is it's own country. It has it's own currency, national anthem, language, flag, accent and animals ( the four horned sheep and tailless cat). The three legs (not arms) refers to the Manx motto.

Which ever way you push us, we shall stand. (We don't do so well side-ways though. Lol)

The eaves crest a;so has three arms any connection?

Found a family name from early 1700's on isle of mann
does anyone know where those people came from?