I'd do a $10 flimsy drugstore stroller for the 3yo and spend a couple of weeks pre-trip "practicing for the airport" with the 3yo riding and 5 and 6 walking without complaining, each with their own backpacks. Do it at the grocery store, walking to the park, on an outing to a museum, etc.

Get a bag of super-ultra-favorite small snacks and dole them out in small increments at every step (not fussing at the ticket counter, making it through security, getting to your gate, waiting nicely for the plane, etc.). One small Matchbox car or similar reward if they do a great job getting to their seats on the plane. One special job for each kid (lead the way, spot our luggage on the carousel, count the carryons to make sure we have them all, pick where to buy extra drinks before flight, etc.).

I would pay absolutely zero attention whether before or during to the preferences of whiny 5 vs. independent 3. This project has to be done your way or it can't happen, because you are the adult.

can you give them an ipad to keep them still while you're doing the things that they need to be under control for? I assume that might make it harder to get them moving again/they freak out when you say "time is up, we're moving on to the car now" or whatever.

walking doesn't seem like the problem. it's staying still. My son at 3 would run ahead of us when heading to our gate but it was never a real issue - we'd keep an eye on him and if you trust one of the older kids have them run up ahead and capture him if he's going too far.