well when i was alone with alex at 4mo (australia to US and back alone) and again at 11mo (NY to london alone) i had te stroller and the pros were i could walk her around in it for a little attempt at sleep etc and i coudl put stuff in it while i carried her at one time, but mostly it was a hinderance with the security issues. BUT then i had her in a pouch at one point on the trip and she was even asleep and they made me take her out of it to run the bjorn thorugh the xray machine - either way there are pros and cons. but i only had her then - with the 2 kids i think i would go the sling so you can load a cart with the luggage and stuff and have the baby on you. when we travelled with both kids (with dh each time) we often had youngest in maclaren and oldest sitting on the pile of luggage on the cart (you do whatever ...)
toys /activities - baby - rattle, small toys; 3.5yo: stickers, colouring book and new crayons, doll, books, small toys you know she likes. mix it up with food - so play for a bit, then have a snack, then read a story, then give a toy, snack etc
we have always spent time walking around - they like to look around (even babies) and people like talking to them etc. win win.
i am gearing up for a trip in 7 weeks involving flying to paris via seoul. this will be new since they are now 5 and 6 1/2yo.i have put aside such a stash of stuff to bring though LOL i always over prepare and i swear 1/2 of it does not get touched. always get used = stickers, colouring supplies, books, etc