This is an interesting question that is not raised very often. The short answer is that the owner is the aggrieved party that could complain about the checkpoint; not the arrestee that has no connection with the trespass. However, there are sometimes ways in which those issues can be utilized to defendant's advantage. A lawyer will be able to research those matters and place your case in the best posture. I recommend that you hire a lawyer?
The information provided herein does not create an attorney-client relationship. The information provided is to suggerst some general principles and should not be relied upon for client decisions. Only upon the hiring of counsel can such advice be custom-tailored to the client's specific situation and needs.
If you're the property owner where the DUI checkpoint occurred or someone the police arrested during this DUI checkpoint, you should contact a local criminal attorney. I have not heard of a DUI checkpoint occurring on private property without the property owner's consent (though I'm sure it happens) but generally the courts have allowed some horrible police abuse with regard to DUI checkpoints. Again, hire a local attorney to examine this matter. Good luck.
By private property what exactly is meant? A driveway? A private road? This is interesting from a variety of standpoints, one would be that certain offenses must be on the roadway or highway. I would contact an attorney who knows how to sue the government for infringing on property rights and start with searching for real property attorney in Sacramento on the AVVO website. Good luck.