It would help to know more about your situation in order to get you the best answers. For instance...
>Where does the father live: in Aruba also, or in another country? If another country, you'll need to explore that country's immigration and/or tourism policies with regards to your children.
>Were you and the father married, and then divorced? If so, the answer to your question may lie in your divorce settlement or the custody court order that came out of the divorce proceedings.
>How does the father feel about the arrangement you describe (i.e., two weeks with you, two weeks with him)? Are you suggesting this as a perpetual cycle in which the children are shuttled back and forth between you every two weeks?
>How about the children: how old are they and what are their wishes? If the children are school-age, are they home schooled (so that the back and forth between you and the father wouldn't be an issue with the school)?