Are you flying alone with the kids or will you have another adult with you? Also, what size is your 2yo (height and weight) and is he or she a reliable walker? Third question is whether you have a direct flight or a layover, and how long are any layovers?
Airlines are not allowed to charge passengers any sort of checked-bag fees (at the ticket counter or at the gate) for passenger assistance devices, which include carseats, boosters, and strollers. That said, you run the risks of damage and loss. These risks are much higher for checked items than for gate checked items, which are handled more carefully and are very seldom lost. Our stroller tends to arrive at our destination a few flights after us when we check it at the ticket counter.
At the very least, I would find a way to transport a light convertible carseat (for the 2yo) and your infant seat or another convertible for your baby through the airport -- you are not required to check your carseats at the ticket counter, even if your baby IS traveling as a lap child (which I don't recommend either, both for very strong safety reasons, and also -- especially if you are traveling alone with the children -- for practicality and your own comfort).
If you make the decision to take the baby as a lap child, try to arrive early at your gate, ask the gate agent whether there is pre boarding for families since you'll be installing a carseat on the aircraft, and then ask whether the plane is full or if there are any empty seats on board. If there are empty seats, ask whether she'd be able to reseat you next to one. Most airlines will allow you to install your other carseat in that empty seat, but there's no requirement that they do this. If you're not able to use an empty seat next to you for the baby's carseat, you will have to gate check it.
If you are installing 2 carseats and are traveling without another adult, generally the carseats will be side-by-side (window and center or aisle, depending on whether it's a 2- or 3-seat row) and you will be in the aisle seat or just across the aisle. Or, if it's a smaller plane with 1 seat on one side and 2 on the other, you'll have a carseat in each window seat and you'll be in the seat between them.
I know the idea of getting 2 little ones and 2 carseats through the airport and installed on the plane is daunting. But it's doable, and when I'm traveling with little ones, which we do a lot, I consider those 5-pt harness my best friends!