So many comments, it just seemed like I should say something too.
I believe that it would be best if Adults did not bring infants into the first class cabin. When traveling with infants (0-12 years old in some cases) they should choose to fly coach. I do not think this should be a law or a rule, just common courtesy.
Why coach? Just like eating at McDonalds, I expect not to have a "leisure/quiet/pleasant" trip in coach but do in First. When I eat at a top end restaurant, I too think Adults should not bring infants...that is why there is Denny's, McDonalds, etc.
First class is special. It is for major business travelers. It is for those who can easily afford the huge expense. BUT must importantly it is for those special occasions where you "shoot your wad" to make everything as perfect as you can for you Honeymoon, Anniversary or ... Same with a first class eatery.
No, no laws or rules, just common sense and courtesy.
As for drunks, etc. They obviously have no common sense or courtesy.