For me, it boils down to basic respect for your fellow travelers, independent of class of service. My experience has been that the problems generally arise with the parents and not the children.
There was the Dad who upgraded his wife and two children, both under three, from PVD-ORD and then demanded that everyone in the cabin move around "to just help him keep his family together." Several folks were willing to help him out until he chastised us for not moving fast enough for his taste. He left his wife and one child in First and went back to coach with the other child so he could get two seats together as no one would help him post-lecture. Also, why should being childless on the flight somehow usurp your right to stay in the seat that you paid for and selected?
Also, the proud Papa who parked one of his six month old twin boys on the seat next to me, not even buckling him in, while he and his wife sat in front of me and the Nanny and the other son sat across the aisle. The FA came by and chastised me for "neglecting my child" and I pointed out that I was childless and where she might find the parents. They turned and insisted that since the seat was vacant, I should watch their son, as they were sure he would be no trouble. The FA promptly returned the child to his proud Papa in time for take off and declared the seat next to me as "unsafe due to a problem with the seat belt."
The greatest, though, was the young lady playing jacks in the aisle while everyone had to step around her and her Mother insisting that she wasn't a bother to anyone. FAs with serving carts had a different opinion. It seems the little darling could only find nine of the ten jacks. Her Mother, fortunately, found the tenth one in the dead of night (FC Suites SFO-LHR) when she stepped on it in her stocking feet on her way to the lavatory. The flight attendant asked to be mindful of the other passengers and please be quiet.
Kids will fuss and cry now and again, but it seems trivial compared to the blather most of their parents produce.