Tell your parents that they should relax (or at least they can bug you about OTHER things!). The lack of a rank will not disadvantage you at all. However, when the time comes, you should make sure that your guidance counselor explains (in your recommendation) why classmates applying to the same colleges that you are will have a rank on their transcripts and you will not.
The biggest disadvantage of switching to a new school in 12th grade is that your “competitor” applicants will probably be boasting of leadership roles in school activities while you will be the newcomer who may not have an opportunity to take on key jobs in clubs and organizations. However, admission officials often tire of seeing the same school activities (and leadership positions) listed on application after application, so perhaps you will be able to highlight interests and accomplishments that didn’t take place in school and will help you stand out in a crowd. In fact, your year abroad might introduce you to atypical endeavors that don’t turn up in most U.S. high schools … or on most applications.
But, meanwhile, don’t worry about the lack of a class rank, and safe travels to you.