Ok, first of all, thanks for the feedback and suggestions. We've talked and brainstormed a bit, and have a few name ideas that we like better than either of the original ideas.
There is "Summer in Trigue", in which case the island would be named Trigue. (Inspired by a similar idea from feedback). What can I say, I like puns and will not apologize for that fact

The other options are "I Can't Get Away From My Romantic Getaway", and the variation that also has the word "Island" in it. Not quite a pun, but still wordplay.
Please note that I've set this new poll to allow you to vote for two choices, so that in addition to voting for which title you like best, you can also vote for whether you think Island should be in the second title.