Isn't it tempting to just go over and poo in the offending neighbor's yard and yell at them, "How do you like it?" While your children and your health should be the most important thing to you, it is not anyone's place in this world to say who or what is more important regarding someone else's life. When cats fell out of favor in Europe, they were eliminated to the point where the rat population went completely out of control resulting in the Black Plague. It's about understanding and tolerance and respect which I am sure is a lesson we want our children to understand. First, you talk to the neighbor. If you feel you are not being heard, talk to the neighbor a second time and tell them it is unacceptable. It is your yard and your rules. There are fencing options for cats. Maybe even let your neighbor know that there are fencing options for cats. You don't have to do the research for them; just state the fact. Then discuss a date that you want the problem resolved. For example, (depending on discussion) "Okay, you're going to look into fencing or build an enclosure and have the problem resolved by date. If there are any delays, please let me know. Thank you." (More bees with honey.) IF no resolution by agreed upon date, you go over, get an update, and if unsatisfied (they really aren't trying) let them know that you're calling animal control. Shooting or trapping the animal is illegal, depending on the state, could cost you a fine and some jail time. It is also a bad example to your children of problem solving and getting along. At the very least, you will have an enemy living near you, just waiting for you or your children to do something remotely aggravating. I had a cat who used the neighbor's mulch for his litterbox. I was unaware. My neighbor told me. It was embarrassing, uncomfortable, and while my cat is an animal, I still felt the same way as a human parent which is "Not my cat (kid)." I didn't want to believe that my cat could do anything wrong. The only thing I could do at that time was keep him in. So that's what I did. He eventually got over wanting to go out and was safer. In addition to apologizing and asking permission to go on the neighbors property with a bag and clean up after my cat, I followed up with my neighbor to make sure I cleaned well enough and that everything was remaining neighborly. I got grumped at that, "yes, everything was cleaned up and I have not seen your cat; but the birds are sitting in the tree and pooing all over my car, the squirrels are digging up everything and the rabbits were eating all the flowers." I could only reply that I couldn't control the squirrels. Today, I have my cats fenced in for their own protection as I have neighbors who let their dogs run so I do understand that it can be frustrating to have neighbors whose concerns are not the same as yours. Sometimes people have something going on in their lives that we don't know about. When my fiance was killed 6 months before our wedding, my head was up my butt for about a year. Some other suggestions for neighbors with roaming cats: enclosed porch, an enclosed gazebo, a sunroom addition, even one of those little boxes that sit in the window, a bay window, a small 10 x 10 framed and wire enclosure with shelves off the back of the house accessed through an existing window/patio door, etc. If you're a handyman, look at it as an opportunity to make a little cash on a side job. To protect your garden, you can also use motion sensing sprinklers. That should scare off the bunnies too. I hope this helps. There's already enough hostility and pain in the world that none of us needs to add to it.