Do you have lab results and reference ranges that you can post for us to look at? My daughter was born without a thyroid in 2000. She began her t4 medication (Synthroid) at 3 weeks of age. I was not told that the thyroid gland was actually absent until she was 1 after an ultrasound and Technician (radioactive iodine) scan was done. Nothing glowed as the thyroid atracts iodine,so no gland there! DO NOT take your daughter off her thyroid medications and switch to anyrhing that is homeopathic. It is, however, past time for your daughter's doctor to take a little closer look so you know what you/she will be dealing with for her life time. My daughter will be on thyroid replacement for the rest of her life. She cannot live without it! Since you're daughter is on 50 mcg on an alternating dose then there is a chance that she also has little or even no thyroid function too, just as my daughter. Get the doctor to do these test/scans to see for sure as you need to know as a parent. My daughter is 10 now and very smart and normal in every way! Gods Blessings to you and yours!
Has your daughter's doctor defined the cause for her being hypothyroid?