I'm pretty sure that Charlote Zeepvat in "The Camera and the Tsars" states that Ekaterina resisted becoming his mistress for a year after she left the Smolny. I believe that the children were orphaned and penniless due to the extravagance of their father and enjoyed the patronage of the Tsar as a result of the regard that he had for their late father.
As Princess Yurievsky, she was renowned for her poise and elegance, and for an air of aristocratic hauteur that seems to have been natural as opposed to studied.
It is said that had Alexander not met such an untimely end, that, in spite of her being his morganatic wife, he may well have tried to make her his official consort.
It is also said that the Yurievsky's rooms were above those of the Empress Maria Alexandrovna, and that she was accustomed to hearing the footsteps of the children as they played on the floor above. By the time of her death I think that she was reconciled to the idea of her husband's second family, and I think had met the children?
The sad fact in all of this is that when the Empress finally expired in 1880, after many years of ill-health, she was entirely alone.................