Hello! Your 4 year old does meet the minimum age and weight for booster use. However, most 4 year olds are not behaviorally mature enough to sit still in a booster. If you think that your dd can handle it (you could take some short car trips in advance of your flight to see), then it is an option. Other things to consider would be, are any of your car rides at your destination going to be times when she might fall asleep? Even good booster riders might fall out of position when sleeping. Or, on the other hand, will there be an adult sitting next to her at your destination? If so, then he/she can help your dd to remember to sit properly.
If you decide that a booster is not a good option, then I'd probably take the lightest of your convertibles (I suspect that is the CA, as you suggested), assuming she still fits.
For getting through the airport, I personally prefer the method of "loading up a stroller with everything possible." So, I take a small stroller and pile on car seats (using bungee cords sometimes to help keep them on there) and ALL the carry-on luggage. For toddlers on down (like your 14 month old), I use a sling or carrier (like an Ergo or Beco). Children older than toddler age walk. If there are two adults, then one pushes the stroller and one wrangles children. But even if you are the only adult with the two kids, the stroller/carrier/walking preschooler method should work.
Other people do the airport other ways, but that is what works best for us.