[BritishPanda]

If you want to observe other classrooms, mention that it is part of your student teaching program requirements. During my student teaching, student teachers were expected to do a couple of teacher observations for each experience. If your cooperating teacher is as sensitive as you mention, saying that won't cause her to get mad since you are only doing what you are required to do. It is worth a try to see what she says. The worst she can say is no.

I didn't have a great student teaching experience and I know plenty of people who also had terrible student teaching experience. One student teacher had such a bad teacher that the principal even tried getting the college to switch the student teacher to a different cooperating teacher. However the one thing I learned about student teaching is teaching is very subjective. Everyone is going to have a different opinion about what makes a good teacher. Ultimately the way you teach your own classroom is going to be completely different from the way another might teach.

I agree with your move on notifying your supervisor. One of the mistakes I didn't do in my placement was holding my supervisor accountable. I'm glad she gave you the ok to do the placement.