doable. not pleasant, maybe, but doable. my mom regularily made a cross continental trip with 3 of us similarily spaced in age. this included two flights of about 8 hours, plus a layover. call your airline and see if they can offer some help with luggage, etc. you might be able to get yourself a nice golf cart ride across the airport too. if your toddler is a runner, you might also consider one of those baby leashes!
My neighbor does it alone every summer with similarly aged kids. From what I remember, she tries to sit close to the bathroom. The hardest time was when LO #2 just transitioned out of diapers, and she had to take the youngest with her every time to accompany #2 to the bathroom. Will you have the baby in your lap? I just flew with my 2.5 yo DS, and videos really help, if you do that kind of thing. With three kids I would definitely consider video players for the older ones, even if its not something you do at home.
I did it multiple times and my first 2 are 30 months apart and the 2nd 2 are 26 months aperture. My monkey in the middle was and still is a really active kid. We never did videos but lots of music, magna doodles and Twizzlers.
...the airline that we fly with has TV screens installed in the rear of every head-rest...which means that every child has their own TV! All of our rules/ideas about minimal TV get thrown our the window when we fly.
...as do our ideas about healthy snacks...I pack whatever will help get us their!
It WILL be a crazy flight, but thank you for your supportive posts.