You are not being petty. She is having an impact on how you plant your own property. If it were me, I'd go for the solid fence along the property line (but do check city and/or county ordinances first!). Sounds to me like, even though you were there first (?), she is trying to tell you what you can and can't do on your own property. That photo you posted of the solid fence with the raised beds looks lovely, although it might be a bit on the expensive side to create!
Hope you can come up with some reasonable resolution without creating a neighborhood war! Such an unfortunate situation!
