Based on the currents I'd say there are 2 major trade routes for Arlia to the Continents...
You're gonna go to the island directly north of the Arlia label and then take that to the east to the western gulf (i think that is the correct term) coast of Acelor
The other route is much longer and you'd head south island hopping to Hemlia and then island hop north to Ascarlia's southern tip... and then from there and for the return trip you'd head west to Acelor, either heading north along it's coast or head south and try to get to the islands and back to Arlia before you drift to far west. That complete journey would probably take 2 or 3 years I'd guess. I'm not knowledgeable the specifics hear but you're talking about a trip that is roughly equivelant to a mixture of the trans atlantic travels of the colonial age along with the ships sent to explore asia which have to take a long, tedious, out of the way journey around Africa and many traders, as I recall, stayed years at their destination before returning home if ever.
The problem you have, considering that is that you haven't defined any of those regions as having anything there to make that type of travel a regular and profitable thing. I'm pretty sure most of these trips made their money on trading with each port of call which in this case there would be tons with island hopping, but that would extend the travel too.
There also lies another problem, the length of time to get between these places would be hellishly long for most of us to contemplate about ^.^ but there is a story to draw from, Helen of Troy and the Trojan War which is what you've pretty much set up, perhaps accidentally, with such travel time between the two nations.
Also, given the currents, Arlia would be fairly easy to get to if they have a fleet on that west coast as it would be a fairly straight shot down for them. It's jsut the way back would be against the currents which is never liked in sailing. So they could deploy quickly but their return would take time.
Question: What is the purpose of the Arlian Prince? Is it love or political power or lust or trying to get one over? And what is the governance of the Empire like? Changing these would change the response as a Princess with no Princes to claim the thrown would give claim to Arlia over the thrown where as with a Prince it would not, at least not directly.