To my knowledge, there's no link to the Lachydrin and the darkening skin. The darkened skin is usually just dead skin that hasn't peeled away yet.
As far as how often to apply Lachyrdin versus a different moisturizer, well, you'll just need to experiment (spelling?). Try putting the Lachydrin on once a day, and the regular moisturizer once a day. Then see if you can move to Lachydrin every other day, with the slot emptied being filled in by regular moisturizer and such.
Also, if you are cautious about applying the Lachydrin on her face, talk to your derm about having the Lachydrin mixed into an ointment by a pharmacist.
For the scalp, try a home made hot oil treatments on the scalp, just as you would for revitalizing your hair. My version of a home made hot oil treatment is to get a ketchup dispenser type bottle, fill it with my preferred oil (peanut oil, canola oil, sesame oil, almond oil, jojoba, whatever your taste or pocketbook prevers,) and warm it by filling a mason jar with really hot water and sticking the bottle of oil in it. I don't like to microwave the oil as it'll get too hot too fast.
Then, I hop in the shower, get my hair wet, comb it all out, and take the bottle with the oil in it and section out pieces of hair so I can gentle squeeze oil directly on my scalp. I don't rinse it out of my hair for at least another 4 hours. Before I rinse it, I comb out my hair with a fine comb and gently remove any loose scales from my scalp that seem willing to come off. Then I go back in to the shower and shampoo my hair at least 2x to get the oil out. Voila! I don't see any reason why this shouldn't work for your daughter, just make sure the oil doesn't get in her eyes as it amazingly can sting the eyes a little bit.
I am female, and was born in 1972 with Lamellar Ichthyosis.