I do feel for you.
There is another way of approaching this problem.
If you are getting nowhere explaining your reasons and providing some evidence of how lovely NZ is and how beneficial it would be for your son as well as yourself, step back a little and 'compromise'. Say you are going for a year or so for the adventure, and will be on the first plane back to Bermuda sooner if things don't work out. You are not really telling an untruth - there might be a teeny tiny possibility of that happening! It is the thought of you living permanently and finally in another country which is probably freaking your family. If you had decided, say, to tour Europe and Asia on a working holiday I bet they would not be so stressed at your decision.
Admit you are scared of the move (even if you are not), scared of being without family support, but need to get out and 'travel' before settling down permanently for your son.
This might not be the right frame of mind you want - I well remember myself the optimism, excitement and determination to make the move successful and final. But it will give hope to your family and, as the months go by, they will find that they are getting on quite well without you around and are looking forward to your letters, photos, or even better blog entries.
I wish we had taken this line of action with my father-in-law who made our lives hell after we had told him of our emigration plans. He took the news so badly that he went on the offensive and did all he could to disrupt our plans. Today he speaks to the children on the phone and looks forward to their letters and photos, and can see they are healthier and happier than they were. My own parents had lived in NZ themselves many years ago, so they could not really make a fuss. I do now speak to, write and email my parents regularly - a lot more than I did in the UK!