Wow...migraines starting at 6 years old! I have a friend who's daughter went through years of them and they discovered it was a problem in her cervical spine. Since they're coming on around 8 in the evening I would pay real close attention to what she is eating... maybe she's reacting to something she's having for dinner on those nights...esppecially since she gets relief after throwing up.
I'm pretty conservative when it comes to kids and cleansing...I would focus on a really healthy diet, some juicing and perhaps some supplemental fiber instead of heavy-duty cleansing. But I would definitely consider a Rotation Diet to see if she has any food allergies /sensitivities.
And stay away from the Tylenol...especially if it gives her no relief. Tylenol can be pretty rough on the liver.