Who is going to Cairo with Tilly instead? Why?

Delphine goes with her. Delphine is far more worldly and sophisticated, accustomed to both wealth and being waited upon. She comes across as somewhat spoiled and selfish, but is also strong willed and independent-minded, determined and confident, all aspects of her personality that rub off not only on Tilly, triggering lasting change, but on Mama as well, for whom the change is not quite so enduring.