Well they have rules about behavior for the lounges now -- children will be allowed so long as they behave. It's a little more difficult on a plane (unless the economy cabin is full) because you just can't kick them off in mid-air. You also cannot get a kid into disciplined mode if they are not used to being in disciplined mode in the rest of their existence.

A partial solution would be some form of compensation for those flying the First Class cabin if the kid was really obnoxious. I know there has been compensation given when there was an obnoxious adult in the forward cabin. A letter on the subject wouldn't hurt. It is possible they would black list the kid just like they black list "air rage" passengers.

A little extreme perhaps but it might send a message to travellers.

I personally don't mind chatty kids and even holding other people's kids while a parent goes to the washroom etc. (as long as it is my choice). Screaming and demanding kids are another matter entirely. It shouldn't matter whether they are in the economy or first class cabin.