Thanks for the reply!
I'm not certain, but believe it's Lan Peru as the flight is from Miami to Lima. And, the fare I want to purchase is Base (cheapest), which is offered on the flights I want. As you know, Base doesn't allow me to select seats. If I want to pay for Base+ (which is also available on the flights), I could.
It sounds like Lan could care less about the safety of my kids on their flights. It's not my kids I'm worried about (they've flown all over the world with great behavior), but mores the strangers Lan would choose to plop next to them.
We tried the whole 'checking in nice and early' bit with another airline in South Africa recently, only to find out that they didn't follow through on what they represented - we couldn't select seats at the check-in window (online or over the phone), so had to plea with the gate agent at the airport. So, my confidence in that practice based on experience is nil.
I do appreciate your candid response, though!
Edited to add that yes, it is my first time on Lan - if we even get on the plane!