Unfortunately, this is happening more and more with equipment changes.

1. Yes, check in online.
2. Use as much self-help as possible: monitor seat map and grab one-off seats as they become available. Focus on grabbing "close" seats, but also good "trading" seats (it's easy to ask someone in the aisle you want to move to another aisle).
3. Watch for seats to become available right at OLCI. I find that seats appear (perhaps because people are upgraded from them?) right at the 24 hour mark.
4. You can ask at check-in, but realistically, they have no more power than you do looking at the seat map. Certainly ask at the gate, and get to the gate on the earlier side.
5. Ask, ask, ask; check, check, check.
6. Prepare the 10 year old and 13 year old for the possibility of sitting alone but nearby. My children are slightly younger than that, and I am using a similar situation as a "teaching experience."
7. If all else fails, politely ask people to switch. But recognize that it's your issue, not theirs. Don't demand -- you have no right to.

Good luck.