About Priceline: If you put in a bid, you don't get to select your flight or seats. You may end-up going on a midnight flight that connects through St. Louis. Priceline does have the standard option of picking a flight based on a published fare.
On the lap ape, the FAA says that children under 2 years old may be considered lap children; they don't need a ticket. Above 2 y.o. needs a ticket. No children under 15 in the emergency exit row, including lap children (infants). That may affect your plans.