The other thing you can do is sprinkle diatamacious earth along the fence between your yard and the flea bitten dog's yard. When the fleas walk through the DE (to get to your yard - yes, they hop, but if they hop through it), they will die as DE is made of finely crushed sea shells and it cuts the flea's legs and they will die. It won't harm your dogs. You do have to reapply after a rain - but it rains so infrequently, that won't be a problem
I have outdoor dogs on both sides of me and I still have no flea problems as long as I use nematodes. The fire ants will still try to live right beside the sidewalks - I guess it is too hot there for the nematodes - but the amount of fire ants is minimal. And there are NO MOUNDS!!!
The first year we put out nematodes, the fire ants went up and were living in our TREE!
It didn't last long though, because they couldn't lay eggs up there!