In regards to the question by mama2four:
I think it depends on why your children are taking piano lessons. If it is just to learn the basics of music, then I think that being self-taught is a fine way to go. A basic knowledge of the piano is a great springboard for all sorts of musical endeavors in a person’s life. Many of the piano courses make it easy for the child to learn on their own once they can read well. If your daughter is musically inclined, then she will probably make it quite far through her books by herself.
However, if your daughter wants to become a good pianist, then I believe that she will benefit from taking lessons from a competent teacher who is musical. There are many, many piano teachers out there who can teach your child to play the piano, but that do not really inspire children to be excellent pianists and musicians. If your teacher is not doing this, then in my opinion, the expense for the lessons is not worth it to you.
If you think that you have found an excellent teacher, perhaps you could continue your older daughter’s lessons, switching to twice month, especially if your teacher will allow your daughters to share a month’s tuition. A bright student can learn quite a bit from one lesson every 2 weeks or even once a month. As the younger children grow, you could have the older daughter teach them the basics of music and the piano. (This would help to solidify her own piano skills as well. You could even pay her a small fee for her services if you think that is appropriate.) If they show a real interest and proclivity to the piano after a few years of the basics, then I would consider formal lessons for them on some sort of a rotating basis.
Piano teachers in general love teaching students who love to learn and who are talented musically. Some of the teachers that I’ve known, including myself, have made special payment arrangements for families who are very dedicated to lessons. You may be able to find a teacher like this in your area.
It’s great that you are making such an effort to include music in your children’s lives! 🙂