First, when you say the fence is partially clearly in your yard and vice versa, what precisely do you mean? How far from the property line is it placed? For instance, are there several feet of your property that are actually on her side of the fence and likewise on your side? Do you know of any reason why the fence was not placed directly on the property line in the first place (or just a couple inches inside it)? Are the lots oddly shaped and this was the only way for the fence to be in a straight line?
Second, who put the fence up in the first place, if you know?
Third, are you sure the reason your neighbor has decided that she likes this fence isn't because either 1) she thinks you'll want her to contribute to the cost and she either can't afford it or just doesn't want to pay (that is, have you told her that you'll pay the full cost?); or 2) she knows that a good chunk of your property is actually in her yard as a result of the present placement of the fence and would like to keep it that way?; or 3) she thinks you want to put up an 8-foot wooden fence that will make her feel claustrophobic?