My standard disclaimer: I am not offering legal advice, assume I do not know the law in your state and that I am just making suggestions. Do NOT rely on anything I write and contact a lawyer in your area immediately for real legal advice.
The Bahamas marriage is valid, remember a lot of folks from the US get married in the Caribbean, the marriages if performed properly with a license etc. are all valid. You need to get yourself to an attorney with a copy of marriage certificate. In any event since you have children, you will need child support and custody, so the attorney or legal aid is well advised.