I'm rather amused that people are suggesting that KA is using this to 'train' her children not to feel 'entitled; seems to me like a bit of an odd way to do it; I think I'd expect a parent doing that to be sharing the privation..
It does strike me, though, that she seems to be 'training' them in the (on the whole, condemned) old upper/middle class belief that children shouldn't expect to have too much of their parents' company or attention.
I think it's really odd that a busy lady like her isn't glad of a bit of time with her children, but that's just my feeling, no-one has to agree with me.