Hut to hut in the Alps

If you are not limited to the US, I highly recommend hut to hut hiking in Europe (or on other places - we have also done it in New Zealand). You may need to reserve the huts on advance and accommodations are fairly basic but generally it is a wonderful experience. And less to carry. Italy was probably best for kids at that age, but really would recommend any of the countries I have done - Norway, Spain, or Slovenia also.