About 3 years ago there was a case where a foreign guy was trying to get custody of his child from the Dominican mother. I seem to remember hearing that he had been waiting to bring the case to court for a few years unthey is lawyer thought they would recognise the child as being old enough to make an 'Independant' decision. I believe the child was 7 years of age. I also believe he didn't get custody.
Whether that has any baring on how a case would go within the country I don't know, that is the only case I have heard of like this.