The restrictions on carseats don't come from the airlines; they are mandated by the FAA. In a nutshell, here they are:
- On US carriers, you are entitled by US law to be able to use a carseat for your child under 40 lbs. if it is approved for aircraft use, AND if you have purchased the seat it will be used in. (You *MAY* be allowed to use it in a seat you have not purchased if there is a vacant seat on your flight, but in that situation the airline has total discretion on whether to allow it.)
- No carseat without an integrated upper-body harness may be used on board an aircraft.
- Approved-for-aircraft-use carseats will have a sticker with RED lettering that says, "THIS RESTRAINT IS CERTIFIED FOR USE IN MOTOR VEHICLES AND AIRCRAFT."
- Carseats may not be placed in exit rows, nor in the rows immediately in front of or directly behind an exit row.
- Carseats may not be installed in a position that will impede egress in an emergency. In practice, this almost always means that they must be installed in the window seat, or in the center seat of a row in the center section of a widebody aircraft. The idea is that no one would have to crawl over it in an emergency evacuation.
- A carseat that a child is actually sitting in during the flight does not count against your checked baggage allowance, but a carseat that is stowed in the hold may count against it -- ask your airline on this one.
If you are taking a carseat on board a legacy carrier flight (not SWA), you should call and let them know about it before you arrive at the airport. If you are assigned an "illegal" seat for the carseat and you don't get it fixed in advance, you chance not having your entire party seated together, because the FA's *will* make you move the carseat to a legal seat.
Oh, about the 5 yo; it would depend on how tall she is and if you still use a 5-pt harness carseat for her. Without a harness the question is moot, as carseats that lack harnesses may not be used in aircraft. IME, kids who are over 4 ft. tall will not be able to sit in a carseat in coach without their legs jammed pretty tightly against the seat in front of them, because the seat tends to force their legs to rest at a bit of an angle against the seat cushion underneath it. We gave up the carseat (on planes) for this reason when DS was about 37 lbs. at age 5.