So to the question: is it normal for teachers to not really insist on finishing a piece like this? Should I insist on making her hear them? I did five songs from grade 3, I did wonderfully well on three, and the other two, well I discussed those above, one was dyanimc contrast problems and the other just note counting issues.
The logic is it doesn't matter as long as you're learning. If you want to spend more time on grade 3 do so. If you want to skip some and move on do so. You'll come across analogous difficulties anyway.
Believe it or not... most teachers want you to progress just as quickly as you can. We have all taught enough grade 1-5 stuff to last us a lifetime. We want you to get to the higher levels ASAP!!!!