You cant just knock her fence down and you cant ask her for half as there is an existing fence already there. What you can do is build your fence hard up on the one that is there - I would do it touching the boundry but all on your side - and she can keep her precious fence while you have your new timber fence. Everyone has a right to fence their property and you have tried to be civil so just do what you gotto do. Not a lot she can do about it. Similarly she could paint the side of her house bright pink and there isnt much you could do about that.