"I was wondering if I could bring someone

over to meet you and your Dad on Saturday?"
"I'll be out," I said, "And he has someone coming?"
"Sunday?" 
"No...."
"Next Saturday?"
"You'd be pushing it," I said.
This was, fortunately, a phone conversation. The person at the other end  could not see my expression. 
She has done this before, more than once. This person is not someone we regard as a friend. She is an acquaintance but she seems to have "latched on". On a number of occasions she has invited herself and someone "you will love to meet" to afternoon tea.
On the first occasion the Senior Cat answered the phone. He thought it was an odd thing to do but he was "polite" and said she could come. I was out - as I often am on a Saturday afternoon. I arrived home and she was still here with her friend. They had been waiting for me to get back. I think her friend was a little  uncomfortable.
The next two "friends" were definitely uncomfortable. They said they couldn't stay long. They had arrived separately and they left long before she did.
The third  "friend" was a little more comfortable perhaps but only just.
"I wish she wouldn't do it," the Senior Cat complained.
He's not being unsociable. He enjoys the company of people he knows. He avoids talking to people with accents he finds hard to understand now that his hearing is not the best.That said,  he will still enjoy meeting someone new if he feels they will have something in common. 
But the people this person insists she wants to introduce are not people with whom we have, so far, had any common interests. We are not likely to have any common interests. Her own interests are quite different from ours.
Middle Cat knows her as well. Being rather more blunt than me she has actually said, "Don't do that to Dad. He doesn't like it." 
The Senior Cat feels his space is being invaded. He feels he should be able to choose who to invite into his home but he has been brought up to be polite. When someone asks him to do something he feels he should do it. He doesn't want to "hurt their feelings".
I put her off by saying, quite truthfully, that the Senior Cat has rather a lot to do at the moment. I reminded her he will be 93 in February and that it takes him much longer to get things done now.
Oh yes, she "understands" and she "will leave it until Feb". 
"Can't she tell we aren't interested?" the Senior Cat asked. He is now wondering whether we have just put off the evil moment or whether he should just ask her "don't do this sort of thing please".
I have, to the best of my knowledge, never invited myself - let alone someone else as well - into the home of someone else for afternoon tea. I wouldn't do it to my friends, let alone a mere acquaintance. It's their space. They should be able to choose who comes into their space.
Is this right - or are we just being unsociable?