As a parent of now grown kids and having been on both ends (my own screaming infant once) and many times adjacent to other crying kids I can sympathize with both the OP and the parents. My spouse and me have carried someone else's baby for a short while to give the parents a break. As long as the parents have made a valiant attempt to calm/control the child, its fine by me. I do get pissed with the I dont give a toss parenting style. Beyond the parents/crews best efforts, not much else can be done. It is public transportation after all. I have had equally worse and some boorish behavior from adults who should know better.
I do recall a friend telling me of a EK F episode where some mid-east royalty/wealthy couple were in a F suite and went to sleep with the door firmly shut while the nanny tried to keep the two kids in control for most of the flight with not much success. At one point he wanted to switch to J to get away from the noise but no seat available.