There are (at least) two possible options here. One is to bring a private civil action against your neighbor for common law nuisance, citing the noise, traffic and dust impacts.
The other, if allowed by state law in Idaho/ is to bring an administrative proceeding against the various municipal boards which may not be enforcing their zoning and building codes, noise ordinances, mass gathering laws and regulations concerning irrigation district water use, after making a due demand, in writing, for each jurisdictional board to enforce its permitting regulations against your neighbor and citing the regulations they are not enforcing.
(In New York State, this proceeding is called an "Article 78 proceeding" and combines several common law "writs" such as "mandamus", the writ used where a governmental agency is not enforcing its laws).
You may get more traction if you can get like-minded neighbors who are also being adversely affected to join with you in petitioning the agencies to enforce their laws or joining your nuisance suit as plaintiffs.
You will probably want to consult with a local attorney who does zoning and land use work.
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In addition to following the options/advice given above, be sure that you have filed a complaint with the City - there should be a complaint process for code violations. Make sure you have exhausted everything with the City. Consider approaching your elected officials to get them to get the City to act as well if they are failing to enforce the code even after you have filed a complaint.
I agree with the answer suggesting a nuisance action as a possible recourse. Idaho has codified nuisance law and the facts you put forth would likely fall under the definition of " nuisance". Additionally, you may want to take a look at the local civil ordinances in your county. Many. Our ties have ordinances that define "nuisance" activities. Finally, you may want to write a letter to your local prosecuting attorney requesting an investigation and possible action by the prosecuting attorney assigned to nuisance abatement.
The first step should be to file a complaint with the municipality. There should be a process set forth in the city zoning ordinance. It may be helpful to consult an attorney to file the complaint for you. I would follow this path initially and if no action is taken, you may be required to file a private action. In any event, I would consult a local land use attorney to determine your best available legal otpion.