Right now, the main hole in their yard is full of rainwater, mud and mosquito larvae. We're had so much rain this year that their construction is running behind. Why they didn't do this back last winter is beyond me. I think at least 15 of their mosquitoes have taken up residence in our house.

You need to do somthing about that ..that can get the whole family sick
if they won't you can call code enforcement from the city you live in and they will do somthing!
West Nile Virus is nothing to fool with the hotter it gets the more likely they are placing you and your family in danger!

check this out;
CDC: West Nile Virus - QA: Prevention