'the airline also has an obligation to the children directly.'
No, they don't. You do. As a parent it is your obligation to keep your child safe on whatever mode of transport you chose to use - be it a car, a train, boat, what have you.
Their obligation is to get all passengers to the destination.
'What's dishonest is advertising tickets at a falsely low price that may result in dangerous seating arrangements, with very small children separated from parents. This should not be possible or legal. '
And they don't! Their advertising is entirely legal. The low price is printed as a figure and then or and * next to it. Fine print in the ad then tells you that add-on services may apply and usually gives T&C or directs people to their website or other form of contact if you have questions.
When you buy the ticket online, you agree to all the T&C. You have to in order to complete the purchase.
If you don't read the fine print, that's your lookout.
I have children, too, if any fucker tries to obstruct my getting off the plane for their own idiocy or acting ghetto, I can promise you, I'll punch their lights out step over them.
Your safety and that of your children on any form of transport is YOUR responsibility, as is the safety of your valuables, etc.