Hello my name is ***** ***** I will help you.
Just to be clear, this is their boundary fence?
Ok - then the neighbour can decide whichever side they want on their side.
There is no right, nor entitlement to the dressed side your side.
I am sorry if this is not the answer you want and certainly not the one I want to give you, but I have a duty to be honest.
Can I clarify anything for you about this today please?Alex