I think Victoria's parents in the video are Jellylorum and the 
younger Asparagus.  During the Invitation to the Jellicle Ball when 
Victoria and Mistoffelees are dancing together, toward the left, you 
can see Asparagus come out of the pipe at stare at them looking 
shocked.  Then Jellylorum comes over to him and tries to calm him 
down.  It's suppose to be a father outraged that his daughter is 
flirting!  Also, during Rum Tum Tugger, Asparagus runs over to 
Victoria to get her to stop dancing at the end. Jellylorum runs to 
Electra, leading me to believe she and Victoria are sisters. 
Jellylorum makes Victoria get away from Grizabella three times.   
Both cats are with Victoria during Memory.  Some of these things go 
by fast so they're difficult to see.  Finally,   During the end of 
Mr. Mistoffelees when he brings Cassandra back, Asparagus and 
Jellylorum are with Victoria and it looks like her father is more 
happy with 

Herald7