Bad idea. You have been misled. There is less support among Gaelic leaders than you think. Divided allegiances make your army weaker than you could imagine.
Use Duguld's influence to get the Gaelic lords on side. If you can unite
the Gaelic and Norse forces, Alexander III would have his work cut
out to defeat you.
Sail down the western seaboard to confront the situation. No Norwegian king has personally visited since 1098. You can meet with Alexander III and hopefully come to some sort of arrangement. Surely there is a peaceful way to settle this volatile situation?
Which card will you play?