I keep hearing "whoever initiates force is wrong" and the point of the government is to be a framework to resolve contract disputes, as well as step in after someone initiates force against someone else.
Joe calls the police and requests he [Bob] be arrested for trespass.
Logic indicates that Joe invited the public (including Bob) in, and throwing him [Bob] out is the initiation of force.
I am trying to answer your question, but you have Joe doing two different things in your story.
If Joe throws Bob out of the cafe, Joe initiated force. And without a context of rights or laws, we do not know if Joe can do this with in the framework of government.
If Joe calls the government (the police) to settle a contract dispute, the government will determine the outcome. If the law dictates Joe must serve Bob, then the government has initiated the force to make Joe cook Bob a meal. If the law dictates that Bob must leave the cafe, then the government has initiated the force to throw Bob out of Joe's cafe. In this case, I assume there's some sort of law the government decide upon and the outcomes are reasonable.
Libertarians holding to the "whoever initiates force is wrong" is a bit silly because the context of the initiation in the framework of the standing government is important. Murdering some one with your car because the person jumped out in front of your car is different than planning to murder and murdering some one because you think the person sneezes too loudly. The intentions of the murderer are paramount to the sentence.
Though one person did send me a link to a youtube video that explains that you can't have personal freedom without property, and it's the personal freedom that is the basis of property, but no explanation of why it works out that personal freedom on someone else's property is determined, in part, but the owner of that property. That circularly comes back to the freedom coming not from personal freedom, but from the property itself.
The act of owning the property is key. If you hop on top of my car while I am in it. I would ask you to get off my car because you are on my property. Your personal freedom is determined by the owner because you do not own the car. I have spent my labor earnings on said car, you have not. We have not entered into a contract verbal or written which states that you may hop on my car.
BTW: There is no true "Libertarian," just like there is no true "Scotsman."