There are some cute family pictures on Berezhnaya's website:
Pictures from her children's baptism (Sikharulidze is Trystan's godfather): http://mamalena.ru/photos.php?id_album=50&main_album=1 (it has a rather un-intuitive UI; you can click > arrow even though the thumbnails on the bottom would have you believe you're done)
http://mamalena.ru/photos.php?id_album=53&main_album=1 - just family pic; some very cute brother-sister moments
There are some other albums here: http://mamalena.ru/photos.php