This is an excellent thread, and a comparable one might be to consider the sisters' relationship with their 'big' sister, Victoria ... grandmother of HRH The Duke of Edinburgh... .
I revere both Alexandra and Elizabeth as Saints, and pray to them as such ... sometimes, the advice I get on a particular issue is, 'Talk to my sister about that - she knows more about it than I do.' In life, however, my heart goes out to them both, because it must have been so hard for Ella to watch Alix in the toils of such an individual as Rasputin, and to be able to do nothing at all to warn her of the very real dangers of such an association. Families often do rupture along just such lines: one member thinks well of someone whom another member sees as the next thing to human refuse, and when religion is so important as it was to these sisters, that the difference should have come about over one who represented himself along religious lines makes it all the more sad. I have experienced something like this, although indirectly, and it is terrible for the people involved. I do not think that Ella and Alix eve stopped loving one another, and the fact that they continued to correspond after 1917 speaks well for them both.
A propos again of Mouchanow, if I may: it was Bob who told me, many months ago, that this book is a fake. But I do not know the rest of the story! If someone does, will you please tell us?
I believe that the 'Elizaveta' who signed the petition for clemency to Dmitri Pavlovich was the widow of 'KR,' Grand Duke Konstantine.