With regard to the Ilyinskys - and I should make it clear I in no way speak for them - I think it unfair to say that they don't care about Russia or their Imperial heritage.
The funeral mentioned was due to the tragic death of Paula Comisar's teenage daughter. I can tell you that Cincinnati, the city where the family lives, is not exactly teeming with Russian Orthodox churches.
Audrey Emery, Paul Ilyinsky's mother, converted to Orthodoxy and Paul's recent funeral was in fact officiated by an Orthodox clergyperson. I honestly don't know if the entire family other than Paula is Orthodox or not, but one funeral does not a non Orthodox family make.
As far as Russia goes, the family has travelled their at their own expense to Russia on several occasions. I cannot imagine what would make any rational person say that they don't care for Russia. Please remember that for most of Paul's life, the Ilyinskys were not welcome there due to a Communist government. Russia became a republic after Paul was over 60 years old!
Yes, the Ilyinskys are now an American family. I know for a fact that Michael Ilyinsky, the youngest of Paul's sons, is very interested in their Imperial heritage, Russia, and Orthodoxy.
The family is aware that Russia is a republic and not interested in a restoration of the monarchy.