Hi D.,
I feel compelled to respond to your post because I am a veterinarian and therefore a public health officer by default. It drives me crazy when people feed cats but don't properly take care of them. Since they are not neutered, they breed, and create a colony who's home base is next door to you!
This is a huge public health issue, especially since you have a little one at home who wants to play outdoors. Cats and dogs when they are not routinely dewormed and are not on a flea preventative are at a greater risk in harboring diseases that can be transmitted to humans.
Children and the elderly are especially at risk since they have immature/weakened immune systems. Children have the added propensity of contracting diseases/parasites because they put everything in their mouths (like dirt infested with cat poop!) and do not wash their hand frequently enough. They love to use sandboxes as a luxury size litter pan! Yuck!!
According to the CDC, 14% of Americans have parasites contracted from their own pets or feral cats/dogs/wildlife. Parasites can migrate through the skin (barefoot walking, crawling around on the grass is a risk factor), but more frequently is ingested (fecal-oral transmission). Fleas can also be a problem. They are usually species specific, meaning they like to stay on a particular host, but if the host is not available, they will jump on the next warm body that passes by: you!
My recommendation is to speak to your neighbor, maybe she does take good care of them (they are all neutered, and on some sort of parasite prevention program). If she denies these are her cats, I would contact a feral cat trapping organization, and or call the health department.
It's not worth risking your child's health over this.
Off my soap box now.
Good luck.