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I am sorry to learn of your difficulty in getting your property zoning application through.
Unfortunately your neighbor is exercising their right to participate in the public political process. If you were to sue them, they would respond with an "Anti-SLAPP" (special litigation against public participation) motion and you would be forced to pay their legal fees for having to respond to your lawsuit.
Zoning is part of the legislative (and therefore public participation) process and you must accept this kind of activity.
I do understand this is probably not the information you wanted to hear, but I do hope that it is helpful (and at least can save you the trouble and expense of filing a suit that will result in you having to pay them!).
I wish you the best of luck with your land use matter.