I gave you a straight and honest answer. It would be foolish to walk outside in that instance as I explained.
Would she be a lawbreaker for (a) shooting him then and there, or (b) threatening him with force if he refused to leave?
Yes to both a and b.
You would be incorrect. The State of New Mexico says this in its Constitution:
Art II, Sec. 4. [Inherent rights.]You see, the warrant is the legal permission/formality authorizing the police to enter your property (without it they are merely trespassers) -- the scenario laid out is one free of any such warrant [S10]. Furthermore, the 'police' rooting around your possessions in no way invalidate your right to protect those possessions [S4]; furthermore, any law trying to disarm you [or restrict your use of arms] to secure your property are null and void [S6].
All persons are born equally free, and have certain natural, inherent and inalienable rights, among which are the rights of enjoying and defending life and liberty, of acquiring, possessing and protecting property, and of seeking and obtaining safety and happiness.
Art II, Sec. 6. [Right to bear arms.]
No law shall abridge the right of the citizen to keep and bear arms for security and defense, for lawful hunting and recreational use and for other lawful purposes, but nothing herein shall be held to permit the carrying of concealed weapons. No municipality or county shall regulate, in any way, an incident of the right to keep and bear arms.
Art II, Sec. 10. [Searches and seizures.]
The people shall be secure in their persons, papers, homes and effects, from unreasonable searches and seizures, and no warrant to search any place, or seize any person or thing, shall issue without describing the place to be searched, or the persons or things to be seized, nor without a written showing of probable cause, supported by oath or affirmation.
So, you see, there are multiple reasons that someone in the situation my mother was in would be lawfully justified in driving the police-officer off (possibly including deadly force). So, being lawfully justified, would be no lawbreaker.