When you have newborns and you're traveling, Johnny recommends bringing your car seat along. You will have to pay for a seat, obviously, but it's worth it safety wise. Always ask if there's an empty row or seat and maybe they won't charge you.
The most expensive day to fly this summer is July 9th, the Sunday after the 4th of July. Sundays are always traditionally more expensive to travel, while Tuesday and Wednesday are the cheapest.