Since nobody lives in NY any more, the question is which state has jurisdiction. The general rule of thumb is that the state where the defendant (your ex) now lives will almost always have jurisdiction, and the state where the plaintiff (you) lives may have jurisdiction.
To enforce a judgment from a different state, most states will have a procedure by which you can file the out of state judgment with your own state, which essentially turns it into a judgment issued by your state. From there, your next step would be the same as it would be had your current state issued the judgment. That would depend on whether or not your ex would be subject to your current state’s long arm jurisdiction statutes. This is simply a fancy way of determining whether or not an out of state resident is subject to your state’s judgments.
Even if the out of state defendant is subject to your state’s long arm statute, enforcing any judgment issued by your state (even a NY judgment which has been converted to an OK one) may still require you to then have the OK judgment filed and converted to a FL judgment.
The same analysis applies to enforcing the stipulation as well. If your ex is subject to OK’s long arm jurisdiction to enforce a contract, then you could sue there, and if necessary, file any resulting OK judgment in FL to enforce it.
In general you can almost always sue your ex in FL.
However, there are two more key factors coming into play.
First is for custody. When multiple states are involved, both the Parental Kidnapping Prevention Act (PKPA) and the Uniform Child Custody Jurisdiction and Enforcement Act (UCCJEA) come into play. In a nutshell, together they say that when there is no prior custody order, the state where the child lives has exclusive jurisdiction over the child absent emergency situations. But once a state has issued a custody order, that state will retain exclusive jurisdiction so long as either parent of the child continues to reside in it. Once neither parent or the child live in the original state, a new state may be requested to obtain continuing exclusive jurisdiction. Normally, this is the state where the child lives.
The rules for jurisdiction over child support are different than those for custody, but they are more in line with the general rule.
You should speak to a local attorney and have him or her review your stipulation and judgment, and decide from there how best to proceed.