I've actually been in a similar situation.
Around this time last year, one of our kitties got sick and racked up nearly two grand (!!!) in vet bills. The SO's family had scheduled a Disney trip for the following summer, to which the SO and I were invited, but no flights, etc. had been purchased yet. The SO wound up going, but I declined, and it was a no-brainer for me. I think if it had been a discretionary vacation, rather than a pre-planned family event where he gets to be Super-Uncle to the nieces and nephew, he would have cancelled as well.
At the end of the day, and this may sound weird but I don't care, I value my pets way more than anything else, including money or vacations. If one of mine were sick with cancer, I would much, much rather stay home with them than go off on vacation and lose more precious time with them -- especially if they're suffering, or if what they have might be terminal. You can reschedule Saint Lucia anytime, but you only get so long with your furry companions, and depending on the prognosis, that time may be running out. If nothing else, I know I'd be worried sick about them while I was away, and I wouldn't enjoy the trip anyway.
So if it were up to me, I'd vote face punch and nix the trip. (And I really hope your dog gets better.)