I'm not so sure the judge could not issue a bench warrant for contempt (just in case Dad gets stopped for speeding on a visit to NY ?)
No. The judge would first have to find the father in contempt. Before she could do that, typically she'd need to issue an order to show cause and have him appear in court to answer. The problem with all of that is that the father is out-of-state, and the court is apparently lacking in jurisdiction over the father. Thus, they can't get a show cause order served and can't compel him to answer. In that situation, contempt sanctions aren't going to happen.
The court could enter the judgment on the previous order that was issued (and presumably the court had the jurisdiction over him back then), which is what the judge did here. Not knowing the full procedural history here, it may well be the case that this is all the NY court could do. In general, you need to use the courts in the state where the debtor has assets or income to collect from his assets and income. In this case, he lives in Florida and thus likely that is where the bulk of his assets and income are located. That's the route the poster will have to go ultimately to collect. It is a cumbersome process, to be sure, but if she follows through she may well see some money from it in time.