The most common cause is thin areas on the sclera allowing the blue choroid underneath to show through.
This is a recent post on blue sclera:
The white part of the eye-the sclera- is normally white and is the outer of the three main layers of the eye "wall". Normally it is whitish in color, under the sclera is the "choroid" the layer that carries the arteries, veins and other blood vessels of the eye. The choroid has pigment cells in it and is dark blue in color, under the choroid and nearest the center of the eye is the "retina". The retina is the sight forming tissue of the eye. The retina is colorless and transparent in health.
When you look at someone's eye you see blood vessels that appear to be on the surface of the sclera. These are in the "conjunctiva" another transparent, elastic tissue that covers the sclera on the surface that we see when we look at someone's eyes. If the conjunctiva is irritated due to allergy, infection, or trauma the blood vessels dilate and the eye looks "blood-shot" or "pink".
The most common color change of the visible sclera is a yellowing that comes with age. This is really a result of the elastic fibers in the conjunctiva yellowing with time and exposure to ultraviolet light from the sun. A yellow thickening often develops at the 3 and 9 o'clock positions called a pingueculum. (a good reason to protect your eyes from extended bright sunlight with a hat and ultra-violet blocking sunglasses).
Now to your specific question. A blue appearance of the sclera is really due to thinning of the sclera allowing the bluish color of the choroid to show through. In older adults there often develops a localized blue spot on the visible conjunctiva called a "scleral plaque". It is not a serious problem and does not require any treatment. When Ophthalmologists (EyeMDs or MD physicians that do medical and surgical eye care) operate on the back of the eye (especially retinal detachment surgery) there are often areas of blue sclera, sometimes rather large, that represent splits or almost absent areas of sclera. These are called "staphylomas".
Diffuse blue sclera results from thinning of the sclera. This might be present at birth or develop in childhood. Blue sclerae are most importantly associated with types I and II osteogenesis imperfecta. Blue sclera may also be associated with:
Ehler's danlos syndrome
pseudoxanthoma elasticum
Marfan's syndrome
Blue sclera may also be acquired through long-term use of corticosteroids.
There is no specific treatment usually done for blue sclera. Diagnosis and treatment of any underlying disease is very important. If a localized area of thinning is about to rupture sometimes a "scleral patch graft" can be used to strengthen the area.
With your daughter's complex history and the excellent job her physicians have done making these unusual and often difficult diagnoses, I'm sure she's seen a pediatric ophthalmologist and an endocrinologist. They would be in the best position to answer your question more specific to her case. I suggest you discuss your concern with them.