I cannot recommend this course of action. Here is the
2017 Match Summary.
OBGYN has only 1,288 positions. In 2017, it was completely filled, no room for even the SOAP. OBGYN PGY-1 has only 23 positions [Table 1]. 105 IMGs/FMGs matched to OBGYN and 0 IMG/FMGs matched to OBGYN PGY-1 [Table 12]. That means OBGYN is comprised of ~8% IMG/FMG and OBGYN PGY-1 is 0% IMG/FMG. More specifically, 64 US citizens from a non-US school matched into OBGYN [Table 2], just under 5%.
As you can see, OBGYN has no trouble filling or almost filling programs. OBGYN competitiveness is considered on the rise. Imagine going through 4 years of medical school, accruing that debt, and not being able to get a job!
Caribbean schools have a high attrition rate--many students don't finish or are forced out by the school (to keep Match numbers high, as these students don't get a chance to apply for the Match). Caribbean schools have subpar resources. Caribbean schools have a stigma. Rule of thumb says Caribbean students need about 10 extra points to match competitiveness, and it's unlikely you will obtain that considering those subpar resources.
It's possible, of course. You could beat the odds. But think of all the students in Caribbean schools. Don't you think every single one of them thought they'd beat the odds?
The problems with Caribbean schools are relatively new--they really arose in the past 10-15 years so it's likely your father does not understand how much worse things are now. The Caribbean was a valid option in the past, but it no longer is.
All applicants should apply to US schools at least twice, with a gap year in the middle to improve chances, at least once to USDO schools, before considering going abroad for medical school.