If I invite my HOA neighbors to my business conference room and one becomes unruly, I will ask him / her to leave. The conference room property belongs to my family. If the disinvited refuse to leave: is the next step to call the police to ask for a trespass warrant in order to have them legally forced to leave? From a legal perspective, is this the proper (effective) action to ask for a trespass warrant to have them removed or is there alternative better legal mechanism?
Police don't issue warrants. Courts can issue warrants (a warrant is a court order directed at a law enforcement officer authorizing a law enforcement officer to do something), but I've never heard of such a thing as a "trespass warrant."
A court could issue an arrest warrant pursuant to a complaint or affidavit filed by a district attorney, but that would almost never be done in a trespassing case.
Police arrest people whom they observe violating the law, and/or for whom they have an arrest warrant issued by a court.
More likely than not, when they arrive, the police would evaluate the situation to see who appears to be in the right, and order someone to leave and only arrest them if they refused to comply. The police could ask you if you want to "press charges" or "file a complaint", but they would not ask you if you want a "trespass warrant".
If it was not obvious who was in the right or there was a dispute over who owned the property, the police would probably separate you and say that it was a civil matter, in which case you could bring a civil eviction action seeking an order for possession which a court would order a law enforcement officer to carry out (via a document called a "writ of restitution" where I practice law) if you prevailed.
UPDATE: Apparently a "trespass warrant" is an archaic term for what is known where I practice law as a "writ of restitution" (terminology that is also archaic). Strictly speaking, the term "warrant" describes a court order authorizing a law enforcement officer to do something, while a "writ" is a court order directing a law enforcement officer or other government official to do something, but people are often sloppy in how these terms are used. It also appears that sometimes the term "trespass warrant" may be used (possibly inaccurately) to refer to what I would call a "notice to quit" (i.e. a formal written demand issued by the property owner or other person with a right to possession that demands that a person leave the premises by a certain time).