Sweetie, I think you should meet the neighbors and ask if they will allow thier children to help you "train" B & J to meet and like kids. Offer to give them little treats and tell them to toss a treat to B or J when they meet them. Tell the children the story about B & J being best friends with the doggie who use to own the house, and they lost their best friend when he had to move when his mommy and daddy bought another house. Kids eat that stuff up and if you talk to them like they are tiny adults (in a kid way) they will get a feeling of being respected by you and will call you their nice neighbor and I think a beautiful relationship will blossom
I could go on and on but I'm sure you get the idea.