That is very strange - completely ignoring a new baby niece/nephew is very odd. Do they ignore the new offspring of other people?
It does seem a shame that these children are growing up with this self-centred role model situation, and that they are not encouraged to take an interest in their cousins. Above all else this would seem to be very unhealthy for them.
As you see lots of their children, maybe when they are with you you could encourage them to write/draw cards/messages for their cousins; or to skype them. Anything that gets across the fact that they are not your only GC and that they could have a role in their cousins' lives.
The fact that they are encouraged to demonstrate their musical prowess, but not to engage with their cousins is a bit puke-worthy - you must be itching to say something! I do not envy you this situation.