Most of this is incorrect - According to IATA regulations the child has to be under two on the first sector - but can be over two on the return (so almost 3 years old even!).

Some airlines will not allow it, but KLM and many others do. I've done exactly this between NYC and Delhi but in business class - I also made sure I was on flights that were not fully booked and had spare seats available.

When checking in for the return they asked about my kids age and said she needed to buy a seat as she was over two years of age - but after checking (at my insistance) they found out it was OK according to regulations.

Again, you have to check with an experienced ticket agent and I would only do this in business class or if you can be 99% sure there will be open seats on that particular flight - not an easy feat these days.