Their coalition is a good idea IF it has teeth and it probably doesn't.

Hit these people coming across the border, suround them and give them a choice of submit and drop weapons or die. End of story.

If they need more bodies, and they do, deputize some men with mil training and experience, have each deputy lead what are essentially squads, 2-3 fireteams apiece.

Seems easy enough.
If they bring in heavy weapons, withdraw initially and then set up reserve forces with appropriate heavy weapons on our side of the border. There is nothing preventing PDs and SDs from obtaining RPGs and beltfeds, grenades, etc.

Slam the door on them hard and they will stop coming.

You can't fight without fighting. It is neither feasible, nor reasonable.