Thank you for your detailed explanation. I was able to reproduce the issue with the multiple parent areas with islands within a single region and get it fixed. I have placed a new SDK build with the fix at http://www.globalmapper.com/GlobalMa..._v134_beta.zip for you to try.
Global Mapper does not support grouping multiple parent areas into a single grouping/region, so when you pull in something like this into Global Mapper the areas will be split into separate regions on export to a new MapInfo or Shape file as the grouping is lost on import.
Let me know if I can be of further assistance.
Global Mapper Support