Yes, I agree so far, I have something to add on the Sicilian part though.
Justin points out that he thinks Alexander III of Scotland adopted the triskelion as the Manx arms because he was in England when the English prince Edmund was offered the throne of Sicily, which has a triskelion in its arms.
Alexander III became king of Scotland in 1249, he was then 7 years old. In 1251, at the age of 9, he got married to princess Margaret of England who was then 11 years old. She was the daughter of King Henry III of England (1207-1272) and as such an elders sister of prince Edmund who was born in 1245. In 1262 Alexander bacame of age, since he was 21 years old, and he resumed his father's project of Outer Hebrides (old norse: Suðreyjar) which was cut short by his father's death 13 years earlier. Alexander laid a formal claim to king Haakon IV of Norway, who rejected the claim. Haakon invaded the Outer Hebrides after having learned that the Scottish nobles had raided the islands in 1262 and that Alexander III planned to conquer the islands. He got assistance from he chieftains of the Hebrides and Man, and ancored outside the Hebrides with 120 ships in July 1263 (12000 - 20000 men). Negotiations was started by Alexander, but he purposely prolonged them. Haakon ended the negotiations and sent parts of his fleet and the fleets of King Magnus of Man (Magnus Olafsson) and King Dougal of Suðreyjar (Dubhghall mac Ruaidhrí) up Loch Long and Loch Lomond to plunder. Then, as Alexander hoped, the storm came (stormy season in september/october) and some of Haakon's ships stranded, and then there was the clash at Largs, which none of them won, but it made Haakon and his fleet to withdraw to the Orkneys for the winter. Haakon stayed the winter in Kirkwall, Orkneys, but he fell ill and died there December 16th 1263.
Now the Islands lay open for Alexander and in 1266 at the Treaty of Perth Alexander and Haakon's son king Magnus VI Haakonson (in norwegian often called Magnus Lagabøte) agreed that Alexander should have the sovereignty over Isle of Man and the Outer Hebrides for the lump sum of 4000 marks and an annuity of 100 marks. Scotland also confirmed Norwegian sovereignty over Shetland and Orkney.
In 1254 the Sicilian crown was offered by the Pope Innocent IV to King Henry III of England. He accepted on behalf of his 9 year old son Edmund. The Pope hated the local king, king Conrad II of Sicily, as hi did his grandfather Holy Roman Emperor Frederick II. But the english king wasn't able to capture the Sicilian kingdom from king Conrad and his halfbrother king Manfred, so the Pope retired the offer in 1263. And that ended the Sicilian story of the Sicilian kingdom.
Edmund, when an Earl of Lancaster and Leicester used a very peculiar seal showing a lion tricorporate which is a lion with three bodies radiating from one head respecting. It is on his seal of 1273 with the legend "Sigillvm Edmvndi Filii". (Source: " A lion tricorporate. In: Dennys, R.: The Heraldic Imagination. London 1975 p. 138: Coll Arms ms. Vinc. 88, fol. 96 (afbeelding van het contrazegel uit 1273).)" This lion tricorporate was perhaps inspired by the Sicilian triquetra and in that case it may have been adopted to the memory of te time he was a pretender of the Sicilian crown. On the other hand it can as well be inspired by the triskeles of the King of Man which apeared in about the same time.
A modern drawing of this lion triskelion can be seen here: http://mistholme.com/dictionary/lion/ It is written "Lion tricorporate (Period)" underneath the Coat of Arms.
I have not been able to find any source sayint that Alexander III used a triskelion.
In 1265 the Pope again offerd the Sicilan throne to Charles d'Anjou and from there on the kingdom of Sicily belonged to the House of d'Anjou until the middle of the 15th century when the House of Castilia Trastamare took over, but lasted just a short time before the Habsburgs took over in 1515.
From Charles d'Anjou took over in 1265 and until the 19trh century, the Coat of Arms of Sicily hav been the Arms of the House of Barcelona where d'Anjou came from and the Arms of the House of Hohenstaufen.
In 1806 Napoleon Bonaparte made his brother Joseph Napoleon Bonaparte King of Naples and King of Sicily. Siting this page: http://www.hubert-herald.nl/ItalTrinacria.htm "Because the quarterly in saltire for Sicilia had always been a dynastic coat of arms, borne by right by the descendants of King Frederick II, it could not possibly be used as a part of the arms of the Two Sicilies of Joseph Bonaparte.
A new emblem was invented for the island, actually not in the posession of Joseph but nominally a part of the newly founded kingdom. For the Island a triskeles or triquetra was chosen as its emblem. It was inspired and based on coins and decorations from Siracusa of the 6th century BC. It was introduced by law of Joseph Napoleon of 1 December 1806 and it was blasoned: Regno di Sicilia: Trinacria d’argento in campo d’oro. That is: For the Kingdom of Sicilia and consequently they are not the royal arms of Sicily."
And that is the history of the Three Legs of Sicily. The rest can be read on these pages: http://www.hubert-herald.nl/ItalSicily.htm
I haven't checked the truthfullness of the sources on these pages, but since there are good sources mentioned and the work look in my opinion to be sound and good, I would trust these alot kore than I would trust Mr. Young's writings.