WTF?
Pardon my french....
Ok, NO ONE in any school. public or private, is even REMOTELY qualified to make an assesment on your child's ability to handle any form of physical activity in regards to a congenital heart defect, PERIOD!
Talk to the surgeon and the cardiologist, get them to write up a simple evaluation of your daughter's condition along with whatever limitations or recommendations they might offer in regards to her participation in PE classes and have that sent to the PE teacher, the principal, the superintendant, AND the school board.
You might also have a copy sent to your attorney if you happen to have one.
If there's one thing that bugs me more than anything else regarding how public (and private) schools handle kids who are not "perfectly normal and healthy" it's in making assumptions based on a lack of knowledge and experience in regards to what a child can and can not phyiscally do in a gym or swimming class. It's dead wrong to do such a thing and it's dead wrong to push a little kid to perform above and beyond their physical abilities.
If they do push your kid like that and she has a heart attack or some other medical emergency that requires a visit to the ER (or worse?) there is a LOT of wide open space for a lawsuit for negligence against the school district and the teacher who pushed her beyond her limits.
All of my teachers in school understood that I had a heart condition and that while I would participate as much as I could in gym class, I wasn't going to perform as well as any other student in the class. I wasn't penalized for it. I did what I could, I even excelled in some things, but when it came to anything requiring a lot of endurance or very strenuous activity, I generally sat it out. Several times a year we'd jog out to the soccer fields and spend 20 minutes playing soccer or jog out to the track and run around the track a few times before going back inside. I generally walked to the soccer field, at a faast pace, and I walked one lap around the track. I couldn't have done any more without ending up in an ER and everyone knew that.
Talk to the doctors and get their official assesments and such and SHOVE IT DOWN THE TEACHER'S THROAT if you have to.
Teachers are wrong to be acting like doctors like that.