Posted: 10/11/2013 at 06:43
Unless it's a cultivated form of ivy the likelihood is that it's grown from seeds dropped by birds and it sounds as if it's been allowed to ramble wherever it likes with no form of control from anyone. There's probably more that one individual plant involved.
I think that in all fairness it sounds like a joint problem and should be tackled jointly - that way you can both control it from your own sides of the fence. If you can see roots/stems clearly on her side of the boundary point it out and explain that it's a weed and you can tackle together.