I represent clients in Raleigh's Child Support Enforcement Court regularly, and see a lot of men who can't get jobs and are months, if not years, in arrears. Often this is an exercise in squeezing blood out of a turnip, which is probably OK for mom's who pay $25 to the county to represent them, and may get a couple of hundred dollars out of the non-paying dad.
Hiring a private attorney to represent you is a different matter. Does dad have money or property that you can get to satisfy the judgment? If not, you may get some personal satisfaction but not much cash. You will need to pay your attorney either way, so some moms could end up deeper in debt, even if they won in court.
In terms of making dad work - that's a good idea that doesn't seem to happen very often. In child support court the judge will threaten dad with jail if he doesn't make a payment to purge himself. This is less likely for alimony arrears. The court can encourage dad to work, but it won't force him to do so.
In terms of dad leaving town - be careful what you ask for. If dad says he has to move a short distance away in order to get a job, and the distance will not harm the child(ren), the court may continue joint custody. I have one client whose 3 year old daughter commutes every other week between Raleigh and west of Charlotte. But if he moves a significant distance, you would certainly have a good argument to press with the court that you should be given sole custody. Good luck.