As a teacher, I will second Jon's advice. I would prefer a parent come to me at the beginning with questions rather than waiting until the frustration point and pulling the student. I would at least like the chance to address the concerns. If I cannot, then they can find a different teacher, and we will probably both be happy with that.

You are asking a lot of the right questions. You will get a number of different answers. Maybe that's why those questions get asked so much. The good part is that you are asking, and you do want your children to continue with (and enjoy!) music.

If I may make a couple of my own suggestions...

#1 Make music a "happy" part of family life. Put on music and enjoy it. Encourage (especially the 7-year-old) to sing or dance with it. Listen to music when travelling. Get your children to put on a special concert for you in your home. Dress up like you're going to a big affair. Basically, have fun. This is the biggest thing that keeps kids in music for life--more than ear training or sight reading.

#2 You are looking for a well-rounded music curriculum. Bravo! PA is a good choice. If you feel that the ear training is still not to the level you'd like (but want to stay with this teacher), you can supplement on your own. Go to the piano with your children and try to "figure out" a favorite song. That's how I learned. Draw their attention to the sounds of music. ("Doesn't that sound just like your last recital song/favorite tv theme/a door bell?") If they try to make up a song or play by ear, gush some praise. They'll do it again... and again and again. And that's how they learn.

#3 Beyond Piano Adventures... still looking to keep their education balanced and complete? Consider the Royal American Conservatory Examinations . Your teacher should not mind since a number of PA songs are on the early lists. This system includes ear tests from the very beginning and advances to college level training. There are resources--including CDs--for preparing the ear.

Enjoy all the music in your house.

Karisofia

P.S. Did I mention having fun? \:D