One thing to remember is that fire ants do not do small colonies unless they are new to the area. The first thing they do is build a deep, deep hive. 5 to 6 foot deep. Once that is in, then you will see small hills that are from side colonies. So you may get one side colony, but still not get the mother hive. So they will keep coming back.
Amdro can work but it takes time and may not get the big hive.
To really get rid of them you have to make a concerted effort to get every single entrance you can find in a single day and lay down Amdro. And pray. Because that may clear most of your yard. But then you need to look again each week and watch for where they start coming back from. That will either be where the main hill is or the guide to where it is. If it is not on your property, you are SOL. All you can do is keep sharp eyes out and deal with incursions as they come. Of course, if they can't spread to your property, they will spread to where they can, so your neighbor may actually do something about it.
If the main is on your property, just keep dosing with Amdro until they are no more. And that may take more time than you think. And the hive will keep trying to spread out and get away through underground paths, so stay alert all over.
It's a war. Not a one and done battle.