I'm Doug, and I'm very sorry to hear of your situation. My goal is to provide you with excellent service today.
The fact that the fence is built, not on the property line, but on your side of the property, means that for her to touch the fence, be it by hand or object, she must necessarily trespass onto your property. This is a civil violation of your property rights as well as a crime and you have two avenues of approach to deal with this.
I might suggest that you begin filing police reports for trespass and criminal mischief. Here is a link explain the crime of mischief: http://www.criminalpropertydamage.com/louisiana/
You may also institute a civil suit for civil trespass as well as for any damage that she might happen to do to the fence. The claim for civil trespass is worth money, even if there is no actual harm done. The harm is presumed in a trespass based on her violation of your right of possession of your property. Here is a link to a discussion of this cause of action under Louisiana law: http://www.lawguru.com/legal-questions/louisiana-civil-rights-law/trespasses-difference-civil-trespass-criminal-848156559/
Finally, under Louisiana law, you and your husband may apply for a court ordered injunction against his sister for the acts of harassment that she continues to perpetrate against the two of you. Here is a discussion of this option: http://www.mahalo.com/how-to-get-a-restraining-order-in-louisiana/
You may reply back to me using the Reply link and I will be happy to continue to assist you until I am able to address your concerns, to your satisfaction.
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I wish you and yours the best in 2015,