well, at the risk of being flamed, no, my kids don't always come first.
eg, two summers ago, my mum was in hospital. My dad couldn't drive as he had just had an op. Visiting times were 3-4 or 6-7.
Great, school pick up or dinner time. Pick up dad and drive him to mum was 1 hour trip.
For 6 weeks my mum came first. of course my kids got lots of attention when i was home, and we did our best to make it work. Dh works form home, so that made it easier (although for him it meant loosing 3 hours work per day, which meant I arrived home, we ate and then he had to go back to work all evening, so I then had to do all kids and then we hardly saw each other)
Kids were young - 6, 9 and 11, but they were amazing. It was good for them to know in a crisis other people's needs come first.
Another example, at times I tutor form home, after school. My kids know that for that hour, they may not interrupt unless someone needs an ambulance. They get this, they understand that at that moment work comes first. Obviously if I did this all the time, they would suffer, but 1 hour 2x per week, is actually good for them to learn about priorities.
Actually, to me it means bringing my kids up to realise that they are not the centre of the universe, and that other people, at times, have needs.