This depends on the lease. Do you use a lease that lists all adults to be living in the unit? I ask my future tenants to list all adults, and occupants(usually the children) as well. An occupant in my state covers anyone that stays over more than three nights. Just tell your potential tenant that if grandma comes from Florida, a preapproved guest can stay one week. Your rights are to know who is living in the unit, and the right to march them down to the local police dept for their criminal report if they have stayed more than three nights......at least in my state. Does the illiegal occcupant receive mail at the address? Are they willing to supply a criminal report? Do they contribute to the rent or utilities? A lot of the younger women do not understand the trouble a supposed boyfriend can cause them.....like losing their rental.
Are you a police officer? Is that how you gain your rights to "march them down to the local PD for their report" comes from. Are you claiming you have arrest and detaining powers as a LL. Seems like you need to read up some more on those state laws.