Maybe the teacher has some point related to the stories about her students.

Introduce them to Piano Street and ask if they saw this thread.
If they're off topic, you can say something like "What about this part?" Ask about something. Or more bold would be to say you want to get through the whole piece this week. They might catch on to a comment like that.
If she's easy insulted, I wouldn't make that comment then, to imply that she's holding things up (even if she is). Just ask a pointed detailed question that needs an answer.
Ah, she's saving the good piano. For whatever reason. Not much you can do about that.
I've heard those ideas about a bad piano. Your supposed to make a bad piano sound good. If you can play well on a bad piano, it will be so great on a good one. Somewhat true, but a bad instrument is a bad instrument. There's only so much you can expect. However, maybe you can figure out how to deal with that problem on the piano. That's tough though with only 30 minutes a week. An hour still wouldn't do it for me though either. That would be a question to ask (and imply the piano sucks but she probably already knows that). Ask how she deals with the particulars of that piano and what you'll need to do to adjust to a decent one (or to adjust to one like they use in a performance situation). Maybe she's trying to save the tuning on the good piano.
Your teacher sounds a bit tempermental to me.
Maybe the teacher is trying to train you to teach? To tell about what her students are doing if the situation is remotely similar. She's probably just tired though and wants to talk.
Maybe just focus on being tactful about steering the lesson back on track. If she's offtopic for real, there are things you can do. Looking at the music, checking your watch, writing something down. In other words, not being quite as good of a listener when she's off topic. It might depends on how she goes off topic. If she just breaks the flow and dives into another topic, I would feel free to throw out a direct question about the piece. If it flows better though something like, "Oh, are they playing a piece by this composer too? Did they have the same issue?" If it's a no, then the teacher might be left hanging. But then you could continue on with a question about the piece.
An easy question is always, "What did you think of how I played this section/spot?" That will either pull the teacher back on track (your track though) or the teacher will ask to have you play it again. Either way, you're back on focus.
It sounds like maybe the teacher isn't thinking too much about you outside the lessons maybe. That's not good, but... what can you do? Maybe you could go in with a list of questions or problem spots. Plop that list up on the piano so it's obvious you have things to talk about and cover (even though that might take several lessons). Then when she's off topic, just dive into the next concern. Some teachers have had my heead spinning when they have certain things they want me to focus on. Whether they thought about it outside the lesson, or whether they just knew during the lesson, either way its on topic and deals with my direction of playing.