I would put colloidal silver on it, let it set a few minutes, then the oil. Help prevent any secondary infections, and is a broad spectrum antimicrobial, might just clear up the cradle cap itself.
And maybe slip a little coconut oil into the diet? My suspicion is that cradle cap is a sebaceous gland issue, and good healthy fats INSIDE her will do more good than on top of her if that is the case.
Adorable little raiders!