I would have a lot less patience than you've shown. (My irritability is less well-controlled.) The first thing that comes to my mind is to wonder what kind of training, if any, does the agency give to its volunteers. This could be a systemic problem, whereby you'ld have to be really lucky to get someone decent from this agency.

You write so well and sound like someone with whom a visitor could have a very appropriate and pleasant and intelligent conversation. (I really do suspect that you might represent this agency better than the characters they are sending out.) Is there any other agency that offers something like this? You might investigate that option. If there isn't, then you would be well within your rights to candidly tell whoever supervises these visitors exactly how inappropriate they are being with you. The person you have coming around now sounds like a lost cause. I would let her go. The next person they send might come with an attitude based on agency gossip that you have complained. But not necessarily. The agency might go out of their way to send you the best person available, knowing that you will not accept poor behavior, which is what they are displaying. I mean not even common courtesy.