Patio Fence Problem

I can't imagine any scenario where I would willfully move in to a place with a shared outdoor space. The big questions are, is there anyone who can order you to take it down (landlord, neighborhood association), and do you want to respect the fact that the shared deck is just as much your neighbor's as it is yours?

Assuming the answers are no and yes, respectively, you would do whatever you could in order to have your privacy while accommodating your neighbor. Perhaps that could be making sure that both sides of the partition are finished, and of good quality. Why would you not want her to paint?

Shared anything is always a road to a gunfight in this USA.
You should have sat on down with her and have had two or three options other than a ratty fence. Did you really want to piss her off?
Is it too late or have you two destroyed all communications by both acting a little childish.
Why would you fence off her property with crappy woad showing on her living side?
I would have considered a bigass planter with climbing things like Manevilia or red flags to attract hummingbirds. Or several potted cedar trees in a line.(They grow your and her privacy with some nic plants.

Surprised you didnt consider a porch garden to share some veggie growing .
Why cant she paint it without your permission?? I dont unerstand your sene of entitlement. You put the thing up without even talking to her. I assume its on her line so I hope she says"why do you have the right to deny me my right to paint it?".

Have you read your CC&R’s? Your homeowners association can force you to take the fence down if it wasn't approved first.