S.,
As a former flight attendant, it is not worth saving a couple hundred bucks nor the inconvenience factor to not buy them a seat and put them in a carseat. F/A's are always pushing to get a law passed that would require it. If it's required by law to have them strapped in for the road where the speed limit is 70mph on the highways, it should stand to reason that at 500mph, they should be strapped in. There are many instances where you can hit a pocket of air that is not predictable to the pilots. It can cause a sudden drop of a thousand feet or more. Flight attendents standing in the isles will hit the ceiling and come down on the seats/passengers and many broke hips with the way they come down. It is quite common even though it doesn't hit the news. I've seen lap children hit the ceiling and come down and get injured too.
In an emergency landing (God forbid), if there are no seats available to strap them in, they are placed on the floor at the bulkhead with pillows and blankets around them. It is impossible for anyone to hold them when the plane is turbulently landing. Our emergency training showed just horrible things that happen to lap children. In the Sioux City crash, 3 of the 4 lap children did not survive. The fourth miraculously flew into an overhead bin that opened, luggage flew out and then closed again.
Children sit better for the parents if they're in their own little seats. Bring lots of little books and small soft toys that aren't too heavy to pack. Even load your ipod with kids songs and they'll get a kick out of that. Also ask the f/a's to warm up a bottle for take-off and landing. We used to do this by putting the bottle in an airsickness bag filled with hot water. The warm liquid while they're swallowing helps to open up their ears and help them not hurt on ascent and descent.
The kids who don't have carseats always had more trouble than those who don't. Plus, you get to board first with little ones. And I always wait to get off last so that we're not standing in the aisles with all of our stuff and antsy kids in tow.
Hope you have a great trip!