Is it against the law to operate a motor vehicle on your own property?

You can not be charged with OWI if your driving is not on areas open to the public. The answer may depend on particular specific facts. Consult a skilled lawyer to review all the relevant details.

Well if the property is not open to the public, then it is not illegal in most States.

The law states that it is illegal to drive under the influence of alcohol or drugs on a highway or other place open to the general public or generally accessible to motor vehicles, including an area designated for the parking of vehicles. So you could be charged with operating while intoxicated if you were driving on the private property of a business that had the property open to the public. But if you are the property owner, you are on your own property, and it is residential property I do not see how you can be charged. I am sure that there are many facts that a criminal defense attorney would like to know. While you say that you never left your property, I want to know if for just one second you left your property? You should hire an attorney.

Yes you can. This issue has already been decided in the affirmative by the courts.

Unlike common traffic offenses that are not enforced on private property, the DUI statute in Utah reaches onto private property, even inside your garage. If you are in actual, physical control of a motor vehicle while over the limit, even if not drunk, you can be arrested for DUI.