Do your kitties have indoor litter boxes? Just because a cat goes outside does not mean they do not need an indoor litter box. Please get two and place them in your house and see if this helps. You have diagnosed that it is nothing medical, but you haven't had a vet check her out. You say she is urinating in your neighbor's house? What is she doing there?
You first start with a urine analysis at the vet. Nothing wrong medically? Then something has stressed her out. All bengals are territorial -- and you've mentioned aggressiveness toward your other kitty! Since she is an outdoor cat, there could be other outdoor cats stressing her out. Has anything changed in your household? Did you move furniture around? The least little change can upset a kitty. You need to take a look at where she is peeing and why that is so much to her liking. The areas need to be cleaned completely with an enzyme cleaner such as Natures Miracle. You may want to check out Jackson Galaxy's Spirit Essences
http://store.jacksongalaxy.com/category-s/1876.htm and see if there is something there that might help your baby.
Inappropriate peeing is the #1 complaint from cat owners. There is always a solution unless the kitty is quite elderly or sick and has lost control of their bladder. Your baby is young! You're going to have to take the time to "think like a cat" and look around your home and see if you can figure out why your kitty is doing this.
Good luck.