Didn't see the swinging cot on the Siberair IL-86 from Novosibirsk to Moscow but that was 4.5 yrs ago.
In the U.S. the seatbelt extensions (Belly Belts) and booster seats are verboten. See the Federal Aviation Administration Civil Aeromedical Institute web site (start at faa.gov or use Google or some other search engine) and be prepared to get the wits scared out of you with video of 3yo size crash test dummies in 16G decelerations. The car seats come right out, up and off the aircraft seats so much that in many cases the child would be smashed right into the seat in front, especially in coach.
The way in U.S. is car child safety seat that meets federal motor vehicle safety standards is used in the aircraft. When you use car seat it must go in the window seat and is not allowed in the exit isle (obviously) On the lap is allowed, but there is no way a parent can hold a baby, much less a child in a 16G crash. After the child is 40# can use the aircraft seatbelt.
As for conduct, you are on your own. Lots of snacks, lots of toys, soft cuddlies, majbe they 'll go to sleep. If teething, I found a finger of Bacardi Dark works well on the oldest, middle didn't like it at all, and the youngest was partial to Johnny Walker Black.