SHE'S BACK!
In the end I waited 'til they came home and me and my neigbour were in the garden talking about how we were waiting for the police (knowing they were next door and could hear us). We went into the house and 10 mins later lo and behold, I hear Kiara meowing outside. She was trapped in their garden so I just climbed over the fence (about 6ft) and got her back.
She was really really noisy and obviously frightened. She was starving hungry aswell when we got her in.
Tucker has stopped crying, he must be happy she's back too. I don't know what to do about the neighbours at all, but i'll have to watch every single one of my pets like hawks. I am looking to move out this year or next anyway, but maybe sooner rather than later now.