Why does my cat keep running to the neighbors?

You needed to walk the cat around the boundry of your house letting her know that this is her teratory. I have done that with all of the cats that i have ever had. I don't know if it is too late to train your cat to recognize the boundry of your yard but the cat doen't know that you don't own the other house as well. Cats like certain spots to lounge like kids an their cafateria. They get over a spot after a few months and find a new one. But you should have walked the cat around your house every day for a few days for about 4 laps. Make sure that the cat is walking not you carrying the cat and walking. Get a leash for the cat and do this.