There are Scarecrow sprinklers and cat repellents available but with kids around I don't feel these will do you much good. A big jar of chili pepper sprinkled throughout the beds????---but you still have to keep tabs on your son touching it. Other than you monitoring 24/7, I think you are limited.
The other issue altogether is having the neighbor take responsibility for it. If the cats need to be outdoors, then your neighbor needs to keep them in his/her yard. I would address it directly with them and let them know you will be either calling animal control or setting live traps (~$75 at Lowes/Home Depot) if the problem isn't resolved within a period of time.
As far as diseases and cat poop, there is a lot of info out there about toxoplasmosis. If you are diligent in removing the cat feces from the area, daily to every other day, the parasite will not reach it's infectious stage. There are also other parasites depending on what's prevalent in your area, the age of the cat and the status of the cat's immune system. I would also encourage regular handwashing after anytime he is outside, but I am sure you knew that. :0)