xpd:
TLDR entire thread ;) Also been driving all day so brain not working...... please note all below is just my opinion and in no way infers any knowledge of council bylaws etc.
If it were me, Id be asking as to why they require the new fence - if its for a dog, then thats their problem, they can build it on their side, or replace existing at their cost. If its for privacy, then I could kinda see why they would approach the neighbors, but again, could just be built on their side of the existing fence.
Height wise, I think 2m is the max most councils allow without having to get permits etc - as long as it doesn't block someones view etc.
We have a fence that is on a shared drive way, and needs replacing, but Im not approaching the other users of the driveway for financial assistance (I could see them offering to chip in but its only because theyre good neighbors) , as its our choice to replace it to keep our dog safe.
If they cant give a valid reason as to replacing the fence, Id have a chat with the council/CAB and see what they say.
I believe they want to keep their dog in as well as for privacy reasons. The existing fence should serve its purpose for keeping the dog in (there might be a couple of small holes need fixing).
What is unclear is the 2m height limit, do you measure it from the lower side of the retaining wall (my side) or from the top of the retaining wall (neighbour's side)?

