I once had to wrangle a duffle type suitcase/bag/dealio into the overhead... damn thing had the girth and weight of a baby hippo and it began to look similar to a MMA fight. I think those in the back were making bets. On that flight was a woman with a youngster and about 6 month old twins. She had a collapsible stroller that the attendant helped her with. The kid was about five or six and gave me PTSD. If she were mine, I'd of duct taped that heathen from mouth to toes into the seat.
Yes, well, among frequent travelers of a certain age and bearing, I think there's something of an unwritten code/commandment to which we all adhere. Call it an "understanding" or "commitment" if you want. Whatever you call it, the fact is that when unruly children's parents fail to exert due control over their kid during a flight, someone else has to. I've done it. I've seen others do it.
There's no specific action to take; what to do depends on the situation, the child and the parent(s). Most often, the thing that I've found that works best is to simply greet the child and ask him/her what's wrong that they can't sit still of keep the volume down. Nine of ten times, just doing that gets the job done, most especially when the child observes their parent not rejecting our "offer" of assistance. I think, perhaps, a "wave" of "oh, sh*t" enters their mind and they determine that while their parents will let them get away with "whatever it is they are doing," there are others on the plane who will not.
I've had multiple parents thank, me and tell me that the kid was afraid of me after I spoke to them. I just reply "You're welcome. It's probably good they fear someone. I don't mind it being me, as long as it keeps them in their seat and speaking at a 'normal' volume." On other occasions, I've "bribed" parents with a variety of things, usually cocktails, but I have used money ($50 or $100, depending on which bill I have in my pocket) delivered at the end of flight and other things. Whatever tack I use, I just know I'm not going to sit on a plane for hours on end and make no effort to get that child back to a state of "calm." Neither am I going to sit idly by while some hooligan with inept parents runs up and down the aisles, especially in the ones of the cabin section I'm in.