Welcome! You'll find the number of questions increase greatly for an extended period as you begin to learn the things you didn't know you didn't know. There is a lot here to help you along so you'll find your situation is not all that new here though everybody is a little different and there are many ways to take off to the islands. A million little details and it's something we do well here. Settle in and take your time.
Boatman61 outlines the idea of working accurately. You need to get familiar with customs
and immigration rules as you skip between national borders. It's all a happy place but there are formalities and laws to deal with. For the most part you need to work under the political radar
since you'll be an undocumented worker. Services pay better than labor. Locals will work for a fraction of what you'll be happy with. A mixed bag of skills really would serve you best. Competing with locals for local jobs might not win friends. Getting along would be a most prized skill.
Will my two fairly large dogs (both around 80 lbs, and very well behaved) present much of a problem?
Depends if they can sail better than you can. Dogs just want to be with you so will follow you any place. We sail with two small dogs and one gets sea sick and the other is pretty good. You can't tell which dogs will and which ones won't. Like people they can get used to it. They can take medication for rough weather
. Over the counter Allergy pills work somewhat. They make a better prescription from your vet but it needs a long lead time. Ease them into sailing with short trips first and just see how it goes. They need to learn about being on a boat just like you did.
Note: Bringing dogs ashore just isn't going to happen officially in other countries. Customs regulations
should be reviewd for every country you visit. It's not something you want to get caught at without proper procedures / papers. While it may not be easy to get caught the implications if you are won't be pleasant.