The right to property means that you are free to do with your own property as you like, so long as you do not infringe on the rights of others.
I think most everyone can agree that right to life trumps all.
So, now we must decide which order to put the other two rights in; property then liberty, or liberty then property. If we say that liberty trumps property, then that means that my right to move about freely is more important than someone else's right to property. To me, it seems like property overrides liberty in the sense that you have to make the choice between coming on my property and possibly forfeiting some of your liberties, or keeping all of your liberty but having to go somewhere else (your own property or the property of someone willing to tolerate your behavior).
Now, in both of these cases we have undesireable side effects. If we let property override liberty then people can be discriminated against. If we let liberty override property then there is no way to be safe and secure in your property and posessions, nor is there any way to remove undesireables from your property. It would appear that the bad effects of having property override liberty (again, you're always free to do whatever you want on your OWN property) are not as bad as letting liberty override property.
What about private property versus public accomodation? Are these one and the same, or is my private residence held to a different standard than a shopping mall or pub? If these things are different, how and why are they different and what laws apply?