Originally posted by Nevada Jen
You are not crazy to be nervous. So lets start with getting there. Will you have another adult on the flight with you? If not, you need to call the airline and make sure you can even fly with that many young kids without another adult. Someone is going to have to be in their own row I would think and I do not think an airline will allow this.
They allow it. The whole point of the new Basic Economy (or the ultra low cost airlines like Spirit, Frontier, Ryanair, etc) is to split families up and scare them enough about being sat away from their kids that they'll pony up for seat assignments.

For OP, I'd recommend booking it so that the 3 older kids get an aisle to themselves. I'm assuming the 13 month is going to be a lap baby. You just sit on the aisle seat across from them. They're basically contained in their own aisle.

Just bring bribes. Some for the kids (new small toys, new (to them) activities, etc), some for the flight attendants (a box of chocolates or candy works great), and possibly some for the fellow passengers around you (ear plugs and candy in a small baggy has been done in the past). If you make an effort, most people are decent and will work with you when they see you making an effort.