I Had the similar problem with my daughter. i was very confused how to teach her to play with correct fingers. Our solution was playing all exercises that suggested in SM. She plays them now every time before playing the pieces she learned so far. As time goes by, I have noticed that she started to use all her fingers more easily, instead of just attempting to use 2,3 fingers. And when she learns a new song, she is using her fingers similar to the exercises. And that just comes from practice.