I wound up writing a sequel so I have decided to give you the link and the summary for it.
Summary: Sequel to She Will Be Loved! Carlisle and Esme's world is turned upside down when their little girl is diagnosed with leukemia. How will the family hold it together as Emily's condition worsens? Slightly AU, set before Twilight and after my story She Will Be Loved. I suck at summaries. Triggers: Cancer (I guess). Could be a tear jerker so grab the tissues. Don't have to read SWBL to get it but I do suggest it!