Hi Dimitri--
My mother has in her bookcase an autobiography written by Ileana; at the moment the title escapes me. If someone else has the book they may wish to mention the title; if not, I'll get back to you with the title and publication date within the week.
I remember reading that during the brief 1914 visit of NAOTMAA to Constanza, Ilena took Alexei under her wing, so to speak, but that he and her slightly older brother Nicholas got into some mischief, playing a few little boy spitting pranks.
Ilena was probably the child that pleased her mother the most. She did marry and have a big family, then eventually was divorced and took the veil, living at a convent which is, as I recall, on the east coast of the United States.