Jamaican Needs Advice With Child Support In Miami

I am an unemployed Jamaican woman who is the mother to two American children living with me in Jamaica. I am married to their father,a Jamaican musician,who is a resident alien living in Miami. He is delinquent and unreliable in his monetary and emotional support of my children(maybe partially because he has fathered at least 2 children with other women during our 8 year marriage or maybe because he has 9,maybe 10 children or maybe it's because his priority is the existing child support order brought by the mother of his 13 year old daughter).I am also certain he hides assets/income. Whatever the reason, I need to make stable, reliable arrangements for my children(boy 11yrs & girl 6yrs) as he is listed on both birth certificates and I am willing to do D.N.A tests if necessary. Can I file for a support order and do I it from Jamaica/online? If not what are the steps that I need to go through.

Thanks for your time.