Of course it is rude, what in the hell is wrong with you? It is YOUR dog, so take her to pee on YOUR lawn. You say after two years of "training," you have yet to get her to go to the bathroom in her own yard? Clearly, you have either not trained her or you have no idea how to train her. It doesn't make a difference how "picky" she is. She is the DOG, you are the handler. As the handler, YOU make the decisions for her, not the other way around. She doesn't get to decide where she goes or doesn't go. Trust me, if she has no other options, she will pee in her own yard. She can't hold it in forever. Letting your dog do her business on other people's lawns is BEYOND rude and inconsiderate. It doesn't matter whether or not it will kill the grass, and it doesn't matter how nice or not so nice the lawn may be. The point is that your neighbor's lawn IS NOT YOUR PROPERTY, and you have absolutely no right to allow your dog to trespass on someone else's property and use their lawn as a toilet. It makes no difference if there are other dogs running loose in the neighborhood. If those dogs are becoming a nuisance to your neighbor, that is between your neighbor and the owner of those particular dogs or animal control. You only need to concern yourself with YOUR dog, and being a considerate, responsible pet owner. Stop using other roaming dogs to deflect from your own inconsiderate, irresponsible behavior. Grow up. If you are not mature enough to understand that you should never allow your dog to use someone else's private property as their restroom, you are not mature enough to have a dog in the first place.