First, if i were you, I might send the teacher an email that you are concerned about the amount of personal information she is sharing; whether you like her or not, it's not at all age appropriate for 7 1/2 year olds to hear the details of her child and the medical issues he/she is dealing with. Most 7 1/2 years olds cannot comprehend situations like that and it can be more scary than helpful - especially for children like your daughter who is expecting a sibling.
I'm pretty high risk and have had almost weekly ultrasounds/fetal echocardiograms. I think I've probably had 15 ultrasounds so far. Due to the fact we have no child care options (and my husband travels for work every week), I have brought my 3.5 year old to every single one. Between travel time to the facility and the actual appointments, it turns into a 4 hour extravaganza every week. It's never been an issue - the Maternal Fetal Medicine office understands my situation and has never said that she couldn't come in. My daughter loves seeing her baby sister and hearing the heartbeat. She's fascinated with what's happening inside my body. I also make sure to be well prepared to keep her busy - we have special snacks, coloring books, the iPad (with headphones, of course). She is extremely well behaved during the appointments. We make it into a big adventure, and she actually looks forward to it (I, however, do not, for various reasons)!
The concern about finding out there's something wrong with the baby at the appointments is always a concern - and they have found a couple of things that they are concerned about with the baby and it is sometimes difficult to hide my anxiety about it, but I do the best I can. I don't have any other options. She has never caught on or thought there was something wrong.
If I had child care options, I probably wouldn't bring her, just because of the chance that I could get bad news and it would be easier to process without having to hide my emotions from her - and I would feel the same way if she were older. I guess you have to weigh how much it would impact you and your daughter if you were to get bad news (since she is old enough to realize what is going on) - although most ultrasounds are normal and a great experience.
ETA: In your case, I would probably bring DD to the elective US, but not the actual anatomy scan a few weeks later. At the elective, it's just to find out sex and not diagnostic; they won't tell you if there's something wrong with the baby. I would skip the actual anatomy scan with her, only in case you get bad news; she doesn't really need to be a part of that.